How to find the surface area of a cube - SAT Math
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A cube has a surface area of 10m2. If a cube's sides all double in length, what is the new surface area?
A cube has a surface area of 10m2. If a cube's sides all double in length, what is the new surface area?
The equation for surface area of the original cube is 6s2. If the sides all double in length the new equation is 6(2s)2 or 6 * 4s2. This makes the new surface area 4x that of the old. 4x10 = 40m2
The equation for surface area of the original cube is 6s2. If the sides all double in length the new equation is 6(2s)2 or 6 * 4s2. This makes the new surface area 4x that of the old. 4x10 = 40m2
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What is the surface area of a cube with a volume of 1728 in3?
What is the surface area of a cube with a volume of 1728 in3?
This problem is relatively simple. We know that the volume of a cube is equal to s3, where s is the length of a given side of the cube. Therefore, to find our dimensions, we merely have to solve s3 = 1728. Taking the cubed root, we get s = 12.
Since the sides of a cube are all the same, the surface area of the cube is equal to 6 times the area of one face. For our dimensions, one face has an area of 12 * 12 or 144 in2. Therefore, the total surface area is 6 * 144 = 864 in2.
This problem is relatively simple. We know that the volume of a cube is equal to s3, where s is the length of a given side of the cube. Therefore, to find our dimensions, we merely have to solve s3 = 1728. Taking the cubed root, we get s = 12.
Since the sides of a cube are all the same, the surface area of the cube is equal to 6 times the area of one face. For our dimensions, one face has an area of 12 * 12 or 144 in2. Therefore, the total surface area is 6 * 144 = 864 in2.
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A room has dimensions of 18ft by 15ft by 9ft. The last dimension is the height of the room. It has one door that is 3ft by 7ft and two windows, each 2ft by 5ft. There is no trim to the floor, wall, doors, or windows. What is the total exposed wall space?
A room has dimensions of 18ft by 15ft by 9ft. The last dimension is the height of the room. It has one door that is 3ft by 7ft and two windows, each 2ft by 5ft. There is no trim to the floor, wall, doors, or windows. What is the total exposed wall space?
If broken down into parts, this is an easy problem. It is first necessary to isolate the dimensions of the walls. If the room is 9 ft high, we know 18 x 15 designates the area of the floor and ceiling. Based on this, we know that the room has the following dimensions for the walls: 18 x 9 and 15 x 9. Since there are two of each, we can calculate the total area of walls - ignoring doors and windows - by doubling the sum of these two areas:
2 * (18 * 9 + 15 * 9) = 2 * (162 + 135) = 2 * 297 = 594 ft2
Now, we merely need to calculate the area "taken out" of the walls:
For the door: 3 * 7 = 21 ft2
For the windows: 2 * (2 * 5) = 20 ft2
The total wall space is therefore: 594 – 21 – 20 = 553 ft2
If broken down into parts, this is an easy problem. It is first necessary to isolate the dimensions of the walls. If the room is 9 ft high, we know 18 x 15 designates the area of the floor and ceiling. Based on this, we know that the room has the following dimensions for the walls: 18 x 9 and 15 x 9. Since there are two of each, we can calculate the total area of walls - ignoring doors and windows - by doubling the sum of these two areas:
2 * (18 * 9 + 15 * 9) = 2 * (162 + 135) = 2 * 297 = 594 ft2
Now, we merely need to calculate the area "taken out" of the walls:
For the door: 3 * 7 = 21 ft2
For the windows: 2 * (2 * 5) = 20 ft2
The total wall space is therefore: 594 – 21 – 20 = 553 ft2
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A room has dimensions of 23ft by 17ft by 10ft. The last dimension is the height of the room. It has one door that is 2.5ft by 8ft and one window, 3ft by 6ft. There is no trim to the floor, wall, doors, or windows. If one can of paint covers 57 ft2 of surface area. How many cans of paint must be bought to paint the walls of the room.
A room has dimensions of 23ft by 17ft by 10ft. The last dimension is the height of the room. It has one door that is 2.5ft by 8ft and one window, 3ft by 6ft. There is no trim to the floor, wall, doors, or windows. If one can of paint covers 57 ft2 of surface area. How many cans of paint must be bought to paint the walls of the room.
If broken down into parts, this is an easy problem. It is first necessary to isolate the dimensions of the walls. If the room is 10ft high, we know 23 x 17 designates the area of the floor and ceiling. Based on this, we know that the room has the following dimensions for the walls: 23 x 10 and 17 x 10. Since there are two of each, we can calculate the total area of walls - ignoring doors and windows - by doubling the sum of these two areas:
2 * (23 * 10 + 17 * 10) = 2 * (230 + 170) = 2 * 400 = 800 ft2
Now, we merely need to calculate the area "taken out" of the walls:
For the door: 2.5 * 8 = 20 ft2
For the windows: 3 * 6 = 18 ft2
The total wall space is therefore: 800 – 20 – 18 = 762 ft2
Now, if one can of paint covers 57 ft2, we calculate the number of cans necessary by dividing the total exposed area by 57: 762/57 = (approx.) 13.37.
Since we cannot buy partial cans, we must purchase 14 cans.
If broken down into parts, this is an easy problem. It is first necessary to isolate the dimensions of the walls. If the room is 10ft high, we know 23 x 17 designates the area of the floor and ceiling. Based on this, we know that the room has the following dimensions for the walls: 23 x 10 and 17 x 10. Since there are two of each, we can calculate the total area of walls - ignoring doors and windows - by doubling the sum of these two areas:
2 * (23 * 10 + 17 * 10) = 2 * (230 + 170) = 2 * 400 = 800 ft2
Now, we merely need to calculate the area "taken out" of the walls:
For the door: 2.5 * 8 = 20 ft2
For the windows: 3 * 6 = 18 ft2
The total wall space is therefore: 800 – 20 – 18 = 762 ft2
Now, if one can of paint covers 57 ft2, we calculate the number of cans necessary by dividing the total exposed area by 57: 762/57 = (approx.) 13.37.
Since we cannot buy partial cans, we must purchase 14 cans.
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A certain cube has a side length of 25 m. How many square tiles, each with an area of 5 m2, are needed to fully cover the surface of the cube?
A certain cube has a side length of 25 m. How many square tiles, each with an area of 5 m2, are needed to fully cover the surface of the cube?
A cube with a side length of 25m has a surface area of:
25m * 25m * 6 = 3,750 m2
(The surface area of a cube is equal to the area of one face of the cube multiplied by 6 sides. In other words, if the side of a cube is s, then the surface area of the cube is 6_s_2.)
Each square tile has an area of 5 m2.
Therefore, the total number of square tiles needed to fully cover the surface of the cube is:
3,750m2/5m2 = 750
Note: the volume of a cube with side length s is equal to _s_3. Therefore, if asked how many mini-cubes with side length n are needed to fill the original cube, the answer would be:
s3/n3
A cube with a side length of 25m has a surface area of:
25m * 25m * 6 = 3,750 m2
(The surface area of a cube is equal to the area of one face of the cube multiplied by 6 sides. In other words, if the side of a cube is s, then the surface area of the cube is 6_s_2.)
Each square tile has an area of 5 m2.
Therefore, the total number of square tiles needed to fully cover the surface of the cube is:
3,750m2/5m2 = 750
Note: the volume of a cube with side length s is equal to _s_3. Therefore, if asked how many mini-cubes with side length n are needed to fill the original cube, the answer would be:
s3/n3
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A company wants to build a cubical room around a cone so that the cone's height and diameter are 3 inch less than the dimensions of the cube. If the volume of the cone is 486π ft3, what is the surface area of the cube?
A company wants to build a cubical room around a cone so that the cone's height and diameter are 3 inch less than the dimensions of the cube. If the volume of the cone is 486π ft3, what is the surface area of the cube?
To begin, we need to solve for the dimensions of the cone.
The basic form for the volume of a cone is: V = (1/3)πr_2_h
Using our data, we know that h = 2r because the height of the cone matches its diameter (based on the prompt).
486_π_ = (1/3)πr_2 * 2_r = (2/3)_πr_3
Multiply both sides by (3/2_π_): 729 = _r_3
Take the cube root of both sides: r = 9
Note that this is in feet. The answers are in square inches. Therefore, convert your units to inches: 9 * 12 = 108, then add 3 inches to this: 108 + 3 = 111 inches.
The surface area of the cube is defined by: A = 6 * _s_2, or for our data, A = 6 * 1112 = 73,926 in2
To begin, we need to solve for the dimensions of the cone.
The basic form for the volume of a cone is: V = (1/3)πr_2_h
Using our data, we know that h = 2r because the height of the cone matches its diameter (based on the prompt).
486_π_ = (1/3)πr_2 * 2_r = (2/3)_πr_3
Multiply both sides by (3/2_π_): 729 = _r_3
Take the cube root of both sides: r = 9
Note that this is in feet. The answers are in square inches. Therefore, convert your units to inches: 9 * 12 = 108, then add 3 inches to this: 108 + 3 = 111 inches.
The surface area of the cube is defined by: A = 6 * _s_2, or for our data, A = 6 * 1112 = 73,926 in2
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If the volume of a cube is 216 cubic units, then what is its surface area in square units?
If the volume of a cube is 216 cubic units, then what is its surface area in square units?
The volume of a cube is given by the formula V = 
, where V is the volume, and s is the length of each side. We can set V to 216 and then solve for s.
In order to find s, we can find the cube root of both sides of the equaton. Finding the cube root of a number is the same as raising that number to the one-third power.
![\sqrt[3]{216}= 216^{1/3}=6=s](https://vt-vtwa-assets.varsitytutors.com/vt-vtwa/uploads/formula_image/image/17880/gif.latex)
This means the length of the side of the cube is 6. We can use this information to find the surface area of the cube, which is equal to 
. The formula for surface area comes from the fact that each face of the cube has an area of 
, and there are 6 faces in a cube.
surface area = 
The surface area of the square is 216 square units.
The answer is 216.
The volume of a cube is given by the formula V =
In order to find s, we can find the cube root of both sides of the equaton. Finding the cube root of a number is the same as raising that number to the one-third power.
This means the length of the side of the cube is 6. We can use this information to find the surface area of the cube, which is equal to
surface area =
The surface area of the square is 216 square units.
The answer is 216.
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You have a cube with sides of 4.5 inches. What is the surface area of the cube?
You have a cube with sides of 4.5 inches. What is the surface area of the cube?
The area of one side of the cube is:
A cube has 6 sides, so the total surface area of the cube is
The area of one side of the cube is:
A cube has 6 sides, so the total surface area of the cube is
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A cube has a surface area of 24. If we double the height of the cube, what is the volume of the new rectangular box?
A cube has a surface area of 24. If we double the height of the cube, what is the volume of the new rectangular box?
We have a cube with a surface area of 24, which means each side has an area of 4. Therefore, the length of each side is 2. If we double the height, the volume becomes 
.
We have a cube with a surface area of 24, which means each side has an area of 4. Therefore, the length of each side is 2. If we double the height, the volume becomes
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What is the surface area of a cube with a side length of 30?
What is the surface area of a cube with a side length of 30?
Write the formula for the surface area of a cube.
Substitute the side.
Write the formula for the surface area of a cube.
Substitute the side.
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The surface areas of six cubes form an arithmetic sequence. The two smallest cubes have sidelengths 10 and 12, respectively. Give the surface area of the largest cube.
The surface areas of six cubes form an arithmetic sequence. The two smallest cubes have sidelengths 10 and 12, respectively. Give the surface area of the largest cube.
The surface area of a cube can be calculated by squaring the sidelength and multiplying by six. The two smallest cubes therefore have surface areas
and
The surface areas form an arithmetic sequence with these two surface areas as the first two terms, so their common difference is
.
The surface area of the largest, or sixth-smallest, cube, is
The surface area of a cube can be calculated by squaring the sidelength and multiplying by six. The two smallest cubes therefore have surface areas
and
The surface areas form an arithmetic sequence with these two surface areas as the first two terms, so their common difference is
The surface area of the largest, or sixth-smallest, cube, is
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Find the surface area of a cube with side length 2.
Find the surface area of a cube with side length 2.
To solve, simply use the formula for the surface area of a cube. Thus,
To solve, simply use the formula for the surface area of a cube. Thus,
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Find the surface area of a cube given side length of 3.
Find the surface area of a cube given side length of 3.
To find the surface area of a cube means to find the area around the entire object. In the case of a cube, we will need to find that area of all the sides and the top and bottom. Since a cube has equal side lengths, the area of each side and the area of the top and bottom will all be the same.
Recall that the area for a side of a cube is:
From here there are two approaches one can take.
Approach one:
Add all the areas together.
Approach two:
Use the formula for the surface area of a cube,
In this particular case we are given the side length is 3.
Thus we can find the surface area to be,
by approach one,
and by appraoch two,
.
To find the surface area of a cube means to find the area around the entire object. In the case of a cube, we will need to find that area of all the sides and the top and bottom. Since a cube has equal side lengths, the area of each side and the area of the top and bottom will all be the same.
Recall that the area for a side of a cube is:
From here there are two approaches one can take.
Approach one:
Add all the areas together.
Approach two:
Use the formula for the surface area of a cube,
In this particular case we are given the side length is 3.
Thus we can find the surface area to be,
by approach one,
and by appraoch two,
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Find the volume of a cube given side length of 3.
Find the volume of a cube given side length of 3.
To solve, simply use the formula for the surface area of a cube.
If you do not remember the formula for the test, it is important to draw a picture or to visually conceptualize it. Remember, when finding area of a square or rectangle, you simply multiply the two side lengths. So for a cube in 3 dimensions, you simply have to multiply those three together.
However, a cube is a special case where all three lengths are the same. Thus,
To solve, simply use the formula for the surface area of a cube.
If you do not remember the formula for the test, it is important to draw a picture or to visually conceptualize it. Remember, when finding area of a square or rectangle, you simply multiply the two side lengths. So for a cube in 3 dimensions, you simply have to multiply those three together.
However, a cube is a special case where all three lengths are the same. Thus,
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A cube has given volume 
. What is its surface area?
A cube has given volume
First, we need the side length of the cube. Given that 
, where 
is a side length, we can solve for 
and set 
simply by taking the cube root of both sides.
Then we need to remember or realize that the surface area of a cube is 
because there will be six identical square faces. Plugging in 
, we get 
as our answer.
First, we need the side length of the cube. Given that
Then we need to remember or realize that the surface area of a cube is
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Find the surface area of a cube with side length 8.
Find the surface area of a cube with side length 8.
To solve, simply use the formula for the surface area of a cube.
If this is not a formula you have committed to memory, remember that a cube has 6 faces with equal area. So, start by calculating the surface area of one side (64) and add it 6 times. Thus,
To solve, simply use the formula for the surface area of a cube.
If this is not a formula you have committed to memory, remember that a cube has 6 faces with equal area. So, start by calculating the surface area of one side (64) and add it 6 times. Thus,
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You own a Rubik's cube with a volume of 
. What is the surface area of the cube?
You own a Rubik's cube with a volume of
You own a Rubik's cube with a volume of 
. What is the surface area of the cube?
To solve for edge length, think of the volume of a cube formula:
Now, we have the volume, so just rearrange it to solve for side length:
Next, recall the surface area of a cube formula:
Plug in and simplify to get:
You own a Rubik's cube with a volume of
To solve for edge length, think of the volume of a cube formula:
Now, we have the volume, so just rearrange it to solve for side length:
Next, recall the surface area of a cube formula:
Plug in and simplify to get:
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