Surface Area - SAT Subject Test in Math II
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A water tank takes the shape of a closed rectangular prism whose exterior has height 30 feet, length 20 feet, and width 15 feet. Its walls are one foot thick throughout. What is the total surface area of the interior of the tank?
A water tank takes the shape of a closed rectangular prism whose exterior has height 30 feet, length 20 feet, and width 15 feet. Its walls are one foot thick throughout. What is the total surface area of the interior of the tank?
The height, length, and width of the interior tank are each two feet less than the corresponding dimension of the exterior of the tank, so the dimensions of the interior are 28, 18, and 13 feet. The surface area of the interior is what we are looking for here. It comprises six rectangles:
Two with area 
square feet;
Two with area 
square feet;
Two with area 
square feet.
Add:
square feet.
The height, length, and width of the interior tank are each two feet less than the corresponding dimension of the exterior of the tank, so the dimensions of the interior are 28, 18, and 13 feet. The surface area of the interior is what we are looking for here. It comprises six rectangles:
Two with area
Two with area
Two with area
Add:
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A rectangular swimming pool is 
meters deep throughout and 
meters wide. Its length is ten meters greater than twice its width. Which of the following expressions gives the total surface area, in square meters, of the inside of the pool?
A rectangular swimming pool is
Since the length of the pool is ten meters longer than twice its width 
, its length is 
.
The inside of the pool can be seen as a rectangular prism. The bottom, or the base, has dimensions 
and , so its area is the product of these:
The sides of the pool have depth 
. Two sides have width 
and therefore have area 
.
Two sides have width and therefore have area
The total area of the inside of the pool is
Since the length of the pool is ten meters longer than twice its width
The inside of the pool can be seen as a rectangular prism. The bottom, or the base, has dimensions
The sides of the pool have depth
Two sides have width
The total area of the inside of the pool is
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What is the surface area of a cube with a side length of 5?
What is the surface area of a cube with a side length of 5?
If you were to take apart a cube so that you could lay it flat on a surface, you would be able to see that a cube is just made up of 6 identical squares. The area of one square is the length of the side squared, so the surface area of the cube would be denoted with the formula:
In this case the side length is 5, so plugging that into the formula will get the answer.
If you were to take apart a cube so that you could lay it flat on a surface, you would be able to see that a cube is just made up of 6 identical squares. The area of one square is the length of the side squared, so the surface area of the cube would be denoted with the formula:
In this case the side length is 5, so plugging that into the formula will get the answer.
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Find the surface area of a rectangular prism with length, width, and height dimensions of 
, 
, and 
, respectively.
Find the surface area of a rectangular prism with length, width, and height dimensions of
Be careful not to confuse surface area with volume!
There are 6 faces in a rectangular prism, and we will need the sum of all the areas of each face.
Write the formula.
Substitute the dimensions.
Evaluate each product in the bracket.
Combine the terms of the numerator.
The answer is: 
Be careful not to confuse surface area with volume!
There are 6 faces in a rectangular prism, and we will need the sum of all the areas of each face.
Write the formula.
Substitute the dimensions.
Evaluate each product in the bracket.
Combine the terms of the numerator.
The answer is:
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What is the surface area of a cube with a side length of 
?
What is the surface area of a cube with a side length of
Write the formula for the surface area of a cube.
Substitute the side length.
The answer is: 
Write the formula for the surface area of a cube.
Substitute the side length.
The answer is:
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Find the surface area of a sphere with a radius of 3.
Find the surface area of a sphere with a radius of 3.
Write the formula for the surface area of a sphere.
Substitute the radius into the equation.
The answer is: 
Write the formula for the surface area of a sphere.
Substitute the radius into the equation.
The answer is:
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Find the surface area of a sphere with a radius of 2.
Find the surface area of a sphere with a radius of 2.
Write the formula for the surface area of a sphere.
Substitute the radius.
The answer is: 
Write the formula for the surface area of a sphere.
Substitute the radius.
The answer is:
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Find the surface area of a cube if the area of one of the square faces is 
.
Find the surface area of a cube if the area of one of the square faces is
Write the formula for the surface area of a cube.
The area of a square side is already given. Substitute that as the 
term.
The answer is: 
Write the formula for the surface area of a cube.
The area of a square side is already given. Substitute that as the
The answer is:
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