Calculating the volume of a prism - GMAT Quantitative
Card 1 of 72
What is the volume of a cube whose diagonal measures 10 inches?
What is the volume of a cube whose diagonal measures 10 inches?
Tap to reveal answer
By an extension of the Pythagorean Theorem, if 
is the length of an edge of the cube and 
is its diagonal length,
The volume 
is therefore
By an extension of the Pythagorean Theorem, if
The volume
← Didn't Know|Knew It →
A cube of iron has a mass of 4 kg. What is the mass of a rectangular prism of iron that is the same height but has a width and length that are twice as long as the cube?
A cube of iron has a mass of 4 kg. What is the mass of a rectangular prism of iron that is the same height but has a width and length that are twice as long as the cube?
Tap to reveal answer
Let the length of the sides of the cube equal 1. The volume of the cube is then 1times 1times 1=1. Therefore, the volume of the prism is 2times 2times 1=4. Therefore, the mass of the prism must be 4 times greater than the mass of the cube.
(4)(4)= 16
Let the length of the sides of the cube equal 1. The volume of the cube is then 1times 1times 1=1. Therefore, the volume of the prism is 2times 2times 1=4. Therefore, the mass of the prism must be 4 times greater than the mass of the cube.
(4)(4)= 16
← Didn't Know|Knew It →
The sum of the length, the width, and the height of a rectangular prism is one yard. The length of the prism is eleven inches greater than its width, and the width is twice its height. What is the volume of the prism?
The sum of the length, the width, and the height of a rectangular prism is one yard. The length of the prism is eleven inches greater than its width, and the width is twice its height. What is the volume of the prism?
Tap to reveal answer
Let 
be the height of the prism. Then the width is 
, and the length is 
. Since the sum of the three dimensions is one yard, or 36 inches, we solve for 
in this equation:
The height is 5 inches; the width is twice this, or 10 inches; the length is eleven inches greater than the width, or 21 inches. The volume is the product of the three dimensions:
cubic inches.
Let
The height is 5 inches; the width is twice this, or 10 inches; the length is eleven inches greater than the width, or 21 inches. The volume is the product of the three dimensions:
← Didn't Know|Knew It →
The length, width, and height of a rectangular prism, in inches, are three different prime numbers. All three dimensions are between one yard and four feet. What is the volume of the prism?
The length, width, and height of a rectangular prism, in inches, are three different prime numbers. All three dimensions are between one yard and four feet. What is the volume of the prism?
Tap to reveal answer
One yard is equal to 36 inches; four feet are equal to 48 inches. There are four prime numbers between 36 and 48 - 37, 41, 43, and 47. Since we are only given that the dimensions are three different prime numbers between 36 and 48, we have no way of knowing which three they are.
One yard is equal to 36 inches; four feet are equal to 48 inches. There are four prime numbers between 36 and 48 - 37, 41, 43, and 47. Since we are only given that the dimensions are three different prime numbers between 36 and 48, we have no way of knowing which three they are.
← Didn't Know|Knew It →
A company makes cubic metal blocks whose edges measure 5 inches. The blocks are supposed to be packed in crates 40 inches long, 30 inches wide, and 32 inches high. How many blocks can be packed in one of these crates?
A company makes cubic metal blocks whose edges measure 5 inches. The blocks are supposed to be packed in crates 40 inches long, 30 inches wide, and 32 inches high. How many blocks can be packed in one of these crates?
Tap to reveal answer
Each layer of blocks will be 
blocks long and 
blocks wide, making a layer of 
blocks. The height is 32 feet, which divided by 5 is
so there will be 6 layers of blocks.
Therefore, 
blocks can be packed.
Each layer of blocks will be
so there will be 6 layers of blocks.
Therefore,
← Didn't Know|Knew It →
A given rectangular prism has a length of 
, a width of 
, and a height of 
. What is the volume of the prism?
A given rectangular prism has a length of
Tap to reveal answer
The volume 
of a given rectangular prism is the product of its length 
, width 
, and height 
, or 
. Plugging in the values provided:
The volume
← Didn't Know|Knew It →
A given cylinder has circular bases of radius 
and height 
. What is the volume of the cylinder?
A given cylinder has circular bases of radius
Tap to reveal answer
The volume 
of a given cylinder is the product of its base area 
and height 
, or 
. Since the circular base area 
, we can substitute and plug in the values provided:
The volume
← Didn't Know|Knew It →
A given rectangular prism has a length of 
, a width of 
, and a height of 
. What is its volume?
A given rectangular prism has a length of
Tap to reveal answer
The volume of a given rectangular prism is the product of its length , width , and height , or . Plugging in the values provided:
The volume
← Didn't Know|Knew It →
Ron is making a wooden chest. The chest needs to measure 45 inches by 72 inches by 36 inches. What volume will the chest be able to hold in cubic feet?
Ron is making a wooden chest. The chest needs to measure 45 inches by 72 inches by 36 inches. What volume will the chest be able to hold in cubic feet?
Tap to reveal answer
Because we are asked for an answer in cubic feet, convert all measurments to feet right away
45 inches: 3.5 feet
72 inches: 6 feet
36 inches: 3 feet
Volume of a rectangular prism is given by:
V=l*w*h
So
V=3*6*3.5=67.5 $ft^3$
Because we are asked for an answer in cubic feet, convert all measurments to feet right away
45 inches: 3.5 feet
72 inches: 6 feet
36 inches: 3 feet
Volume of a rectangular prism is given by:
V=l*w*h
So
V=3*6*3.5=67.5 $ft^3$
← Didn't Know|Knew It →
A cube of iron has a mass of 4 kg. What is the mass of a rectangular prism of iron that is the same height but has a width and length that are twice as long as the cube?
A cube of iron has a mass of 4 kg. What is the mass of a rectangular prism of iron that is the same height but has a width and length that are twice as long as the cube?
Tap to reveal answer
Let the length of the sides of the cube equal 1. The volume of the cube is then 1times 1times 1=1. Therefore, the volume of the prism is 2times 2times 1=4. Therefore, the mass of the prism must be 4 times greater than the mass of the cube.
(4)(4)= 16
Let the length of the sides of the cube equal 1. The volume of the cube is then 1times 1times 1=1. Therefore, the volume of the prism is 2times 2times 1=4. Therefore, the mass of the prism must be 4 times greater than the mass of the cube.
(4)(4)= 16
← Didn't Know|Knew It →
What is the volume of a cube whose diagonal measures 10 inches?
What is the volume of a cube whose diagonal measures 10 inches?
Tap to reveal answer
By an extension of the Pythagorean Theorem, if is the length of an edge of the cube and is its diagonal length,
The volume is therefore
By an extension of the Pythagorean Theorem, if
The volume
← Didn't Know|Knew It →
The sum of the length, the width, and the height of a rectangular prism is one yard. The length of the prism is eleven inches greater than its width, and the width is twice its height. What is the volume of the prism?
The sum of the length, the width, and the height of a rectangular prism is one yard. The length of the prism is eleven inches greater than its width, and the width is twice its height. What is the volume of the prism?
Tap to reveal answer
Let be the height of the prism. Then the width is , and the length is . Since the sum of the three dimensions is one yard, or 36 inches, we solve for in this equation:
The height is 5 inches; the width is twice this, or 10 inches; the length is eleven inches greater than the width, or 21 inches. The volume is the product of the three dimensions:
cubic inches.
Let
The height is 5 inches; the width is twice this, or 10 inches; the length is eleven inches greater than the width, or 21 inches. The volume is the product of the three dimensions:
← Didn't Know|Knew It →
The length, width, and height of a rectangular prism, in inches, are three different prime numbers. All three dimensions are between one yard and four feet. What is the volume of the prism?
The length, width, and height of a rectangular prism, in inches, are three different prime numbers. All three dimensions are between one yard and four feet. What is the volume of the prism?
Tap to reveal answer
One yard is equal to 36 inches; four feet are equal to 48 inches. There are four prime numbers between 36 and 48 - 37, 41, 43, and 47. Since we are only given that the dimensions are three different prime numbers between 36 and 48, we have no way of knowing which three they are.
One yard is equal to 36 inches; four feet are equal to 48 inches. There are four prime numbers between 36 and 48 - 37, 41, 43, and 47. Since we are only given that the dimensions are three different prime numbers between 36 and 48, we have no way of knowing which three they are.
← Didn't Know|Knew It →
A company makes cubic metal blocks whose edges measure 5 inches. The blocks are supposed to be packed in crates 40 inches long, 30 inches wide, and 32 inches high. How many blocks can be packed in one of these crates?
A company makes cubic metal blocks whose edges measure 5 inches. The blocks are supposed to be packed in crates 40 inches long, 30 inches wide, and 32 inches high. How many blocks can be packed in one of these crates?
Tap to reveal answer
Each layer of blocks will be blocks long and blocks wide, making a layer of blocks. The height is 32 feet, which divided by 5 is
so there will be 6 layers of blocks.
Therefore, blocks can be packed.
Each layer of blocks will be
so there will be 6 layers of blocks.
Therefore,
← Didn't Know|Knew It →
A given rectangular prism has a length of , a width of , and a height of . What is the volume of the prism?
A given rectangular prism has a length of
Tap to reveal answer
The volume of a given rectangular prism is the product of its length , width , and height , or . Plugging in the values provided:
The volume
← Didn't Know|Knew It →
A given cylinder has circular bases of radius and height . What is the volume of the cylinder?
A given cylinder has circular bases of radius
Tap to reveal answer
The volume of a given cylinder is the product of its base area and height , or . Since the circular base area , we can substitute and plug in the values provided:
The volume
← Didn't Know|Knew It →
A given rectangular prism has a length of , a width of , and a height of . What is its volume?
A given rectangular prism has a length of
Tap to reveal answer
The volume of a given rectangular prism is the product of its length , width , and height , or . Plugging in the values provided:
The volume
← Didn't Know|Knew It →
Ron is making a wooden chest. The chest needs to measure 45 inches by 72 inches by 36 inches. What volume will the chest be able to hold in cubic feet?
Ron is making a wooden chest. The chest needs to measure 45 inches by 72 inches by 36 inches. What volume will the chest be able to hold in cubic feet?
Tap to reveal answer
Because we are asked for an answer in cubic feet, convert all measurments to feet right away
45 inches: 3.5 feet
72 inches: 6 feet
36 inches: 3 feet
Volume of a rectangular prism is given by:
V=l*w*h
So
V=3*6*3.5=67.5 $ft^3$
Because we are asked for an answer in cubic feet, convert all measurments to feet right away
45 inches: 3.5 feet
72 inches: 6 feet
36 inches: 3 feet
Volume of a rectangular prism is given by:
V=l*w*h
So
V=3*6*3.5=67.5 $ft^3$
← Didn't Know|Knew It →
A cube of iron has a mass of 4 kg. What is the mass of a rectangular prism of iron that is the same height but has a width and length that are twice as long as the cube?
A cube of iron has a mass of 4 kg. What is the mass of a rectangular prism of iron that is the same height but has a width and length that are twice as long as the cube?
Tap to reveal answer
Let the length of the sides of the cube equal 1. The volume of the cube is then 1times 1times 1=1. Therefore, the volume of the prism is 2times 2times 1=4. Therefore, the mass of the prism must be 4 times greater than the mass of the cube.
(4)(4)= 16
Let the length of the sides of the cube equal 1. The volume of the cube is then 1times 1times 1=1. Therefore, the volume of the prism is 2times 2times 1=4. Therefore, the mass of the prism must be 4 times greater than the mass of the cube.
(4)(4)= 16
← Didn't Know|Knew It →
What is the volume of a cube whose diagonal measures 10 inches?
What is the volume of a cube whose diagonal measures 10 inches?
Tap to reveal answer
By an extension of the Pythagorean Theorem, if is the length of an edge of the cube and is its diagonal length,
The volume is therefore
By an extension of the Pythagorean Theorem, if
The volume
← Didn't Know|Knew It →