DSQ: Calculating the surface area of a prism - GMAT Quantitative Reasoning
Card 0 of 3
What is the volume of a cardboard box with six rectangular surfaces?
Statement 1: The length and width are each half the height.
Statement 2: The height is ten inches longer than the width.
What is the volume of a cardboard box with six rectangular surfaces?
Statement 1: The length and width are each half the height.
Statement 2: The height is ten inches longer than the width.
To know the volume of the box, which is shaped like a rectangular prism, you multiply the length, the width, and the height together. Neither statement alone gives you those dimensions, just clues as to how they are related. But together, you can form a system of linear equations using height 
and width (and length) 
.
By the first and second statements, respectively,
This system can be solved:
From this, you can determine the length and height, and, subsequently, the volume.
To know the volume of the box, which is shaped like a rectangular prism, you multiply the length, the width, and the height together. Neither statement alone gives you those dimensions, just clues as to how they are related. But together, you can form a system of linear equations using height
By the first and second statements, respectively,
This system can be solved:
From this, you can determine the length and height, and, subsequently, the volume.
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A box with equal length, width, and height has the following dimensions.
I) The diagonal of the cube is 
.
II) The volume of the cube is 
.
What is the surface area of the box?
A box with equal length, width, and height has the following dimensions.
I) The diagonal of the cube is
II) The volume of the cube is
What is the surface area of the box?
To find surface area, we need to know the side length of the box.
We are told the box has equal length, width and height. This means it is a cube.
I) Gives us the diagonal of the cube, from this we can find the side length.
, where s is the side length.
Now we can use the side length to find the surface area of the box.
II) Gives us the volume of the cube, from which we can also find the side length.
From here we can find the surface area.
Thus, either statement is sufficient.
To find surface area, we need to know the side length of the box.
We are told the box has equal length, width and height. This means it is a cube.
I) Gives us the diagonal of the cube, from this we can find the side length.
Now we can use the side length to find the surface area of the box.
II) Gives us the volume of the cube, from which we can also find the side length.
From here we can find the surface area.
Thus, either statement is sufficient.
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Fry recently met a robot known for bending things. The robot wants to make a box out of steel by bending a single sheet of metal. Find the total area of the sheet of metal given the following:
I) The box will be 
long.
II) The box's height will be 2 feet taller than its length, and the box's width will be 
less than its length.
Fry recently met a robot known for bending things. The robot wants to make a box out of steel by bending a single sheet of metal. Find the total area of the sheet of metal given the following:
I) The box will be
II) The box's height will be 2 feet taller than its length, and the box's width will be
Fry recently met a robot known for bending things. The robot wants to make a box out of steel by bending a single sheet of metal. Find the total area of the sheet of metal given the following:
I) The box will be 
long
II) The box's height will be 2 feet taller than its length, and the box's width will be 
less than its length.
This question is a surface area question in disguise. To find the surface area of a prism, we need the area of each side. Begin by using I and II to find each side length:
Length: 36 inches or 3 feet
Height: 
or 5 feet
Width: 
or 
So, we have all our side lengths. Next, use the following formula for surface area of a rectangular prism:
Where l,w, and h are length, width and height
Fry recently met a robot known for bending things. The robot wants to make a box out of steel by bending a single sheet of metal. Find the total area of the sheet of metal given the following:
I) The box will be
II) The box's height will be 2 feet taller than its length, and the box's width will be
This question is a surface area question in disguise. To find the surface area of a prism, we need the area of each side. Begin by using I and II to find each side length:
Length: 36 inches or 3 feet
Height:
Width:
So, we have all our side lengths. Next, use the following formula for surface area of a rectangular prism:
Where l,w, and h are length, width and height
Compare your answer with the correct one above