Nets - ISEE Middle Level Quantitative Reasoning
Card 0 of 40
Which is the greater quantity?
(a) The sidelength of a cube with surface area 
(b) The sidelength of a cube with volume 
Which is the greater quantity?
(a) The sidelength of a cube with surface area
(b) The sidelength of a cube with volume
(a) A cube has six faces, each a square. Since the surface area of this cube is 
, each face has one-sixth this area, or 
; the sidelength is the square root of this, or 
.
(b) The volume of a cube is the cube of its sidelength, so we take the cube root of the volume of this cube to get the sidelength:
The cubes have the same sidelength.
(a) A cube has six faces, each a square. Since the surface area of this cube is
(b) The volume of a cube is the cube of its sidelength, so we take the cube root of the volume of this cube to get the sidelength:
The cubes have the same sidelength.
Compare your answer with the correct one above
Which is the greater quantity?
(a) The volume of a rectangular prism with length 60 centimeters, width 30 centimeters, and height 15 centimeters
(b) The volume of a cube with sidelength 300 millimeters
Which is the greater quantity?
(a) The volume of a rectangular prism with length 60 centimeters, width 30 centimeters, and height 15 centimeters
(b) The volume of a cube with sidelength 300 millimeters
(a) The volume of the prism is the product of its length, its width, and its height:
(b) The volume of the cube is the cube of its sidelength. We restate 300 millimeters as 30 centimeters, and cube this:
The volumes are equal.
(a) The volume of the prism is the product of its length, its width, and its height:
(b) The volume of the cube is the cube of its sidelength. We restate 300 millimeters as 30 centimeters, and cube this:
The volumes are equal.
Compare your answer with the correct one above
Give the volume of the box in cubic inches.
Give the volume of the box in cubic inches.
Use the volume formula, substituting 
:
Use the volume formula, substituting
Compare your answer with the correct one above
Give the volume of the above box in cubic centimeters.
Give the volume of the above box in cubic centimeters.
100 centimeters make one meter, so convert each of the dimensions of the box by multiplying by 100.
centimeters
centimeters
Use the volume formula, substituting 
:
cubic centimeters
100 centimeters make one meter, so convert each of the dimensions of the box by multiplying by 100.
Use the volume formula, substituting
Compare your answer with the correct one above
A cube made of nickel has sidelength 20 centimeters, Nickel has a density of 8.9 grams per cubic centimeter. What is the mass of this cube?
A cube made of nickel has sidelength 20 centimeters, Nickel has a density of 8.9 grams per cubic centimeter. What is the mass of this cube?
The volume of the cube is 
cubic centimeters. Multiply by the number of grams per cubic centimeter to get 
grams, or 
kilograms.
The volume of the cube is
Compare your answer with the correct one above
A rectangular prism has length 24 inches, width 18 inches, and height 15 inches. Give its volume in cubic feet.
A rectangular prism has length 24 inches, width 18 inches, and height 15 inches. Give its volume in cubic feet.
Divide each dimension in inches by 12 to convert from inches to feet:
feet
feet
feet
Multiply the three to get the volume:
cubic feet
Divide each dimension in inches by 12 to convert from inches to feet:
Multiply the three to get the volume:
Compare your answer with the correct one above
The above depicts a rectangular swimming pool for an apartment. The pool is six feet deep everywhere. What is the volume of the pool in cubic feet?
The above depicts a rectangular swimming pool for an apartment. The pool is six feet deep everywhere. What is the volume of the pool in cubic feet?
The pool can be seen as a rectangular prism with dimensions 50 feet by 35 feet by 6 feet; its volume is
cubic feet.
The pool can be seen as a rectangular prism with dimensions 50 feet by 35 feet by 6 feet; its volume is
Compare your answer with the correct one above
One cubic foot is equal to (about) 7.5 gallons.
The above depicts a rectangular swimming pool for an apartment. The pool is seven feet deep everywhere. How many gallons of water does the pool hold?
One cubic foot is equal to (about) 7.5 gallons.
The above depicts a rectangular swimming pool for an apartment. The pool is seven feet deep everywhere. How many gallons of water does the pool hold?
The pool can be seen as a rectangular prism with dimensions 50 feet by 35 feet by 7 feet; its volume in cubic feet the product of these dimensions, which is
cubic feet.
One cubic foot is equal to about 7.5 gallons, so multiply:
gallons.
The pool can be seen as a rectangular prism with dimensions 50 feet by 35 feet by 7 feet; its volume in cubic feet the product of these dimensions, which is
One cubic foot is equal to about 7.5 gallons, so multiply:
Compare your answer with the correct one above
Which is the greater quantity?
(a) The sidelength of a cube with surface area
(b) The sidelength of a cube with volume
Which is the greater quantity?
(a) The sidelength of a cube with surface area
(b) The sidelength of a cube with volume
(a) A cube has six faces, each a square. Since the surface area of this cube is , each face has one-sixth this area, or ; the sidelength is the square root of this, or .
(b) The volume of a cube is the cube of its sidelength, so we take the cube root of the volume of this cube to get the sidelength:
The cubes have the same sidelength.
(a) A cube has six faces, each a square. Since the surface area of this cube is
(b) The volume of a cube is the cube of its sidelength, so we take the cube root of the volume of this cube to get the sidelength:
The cubes have the same sidelength.
Compare your answer with the correct one above
Which is the greater quantity?
(a) The volume of a rectangular prism with length 60 centimeters, width 30 centimeters, and height 15 centimeters
(b) The volume of a cube with sidelength 300 millimeters
Which is the greater quantity?
(a) The volume of a rectangular prism with length 60 centimeters, width 30 centimeters, and height 15 centimeters
(b) The volume of a cube with sidelength 300 millimeters
(a) The volume of the prism is the product of its length, its width, and its height:
(b) The volume of the cube is the cube of its sidelength. We restate 300 millimeters as 30 centimeters, and cube this:
The volumes are equal.
(a) The volume of the prism is the product of its length, its width, and its height:
(b) The volume of the cube is the cube of its sidelength. We restate 300 millimeters as 30 centimeters, and cube this:
The volumes are equal.
Compare your answer with the correct one above
Give the volume of the box in cubic inches.
Give the volume of the box in cubic inches.
Use the volume formula, substituting :
Use the volume formula, substituting
Compare your answer with the correct one above
Give the volume of the above box in cubic centimeters.
Give the volume of the above box in cubic centimeters.
100 centimeters make one meter, so convert each of the dimensions of the box by multiplying by 100.
centimeters
centimeters
Use the volume formula, substituting :
cubic centimeters
100 centimeters make one meter, so convert each of the dimensions of the box by multiplying by 100.
Use the volume formula, substituting
Compare your answer with the correct one above
A cube made of nickel has sidelength 20 centimeters, Nickel has a density of 8.9 grams per cubic centimeter. What is the mass of this cube?
A cube made of nickel has sidelength 20 centimeters, Nickel has a density of 8.9 grams per cubic centimeter. What is the mass of this cube?
The volume of the cube is cubic centimeters. Multiply by the number of grams per cubic centimeter to get grams, or kilograms.
The volume of the cube is
Compare your answer with the correct one above
A rectangular prism has length 24 inches, width 18 inches, and height 15 inches. Give its volume in cubic feet.
A rectangular prism has length 24 inches, width 18 inches, and height 15 inches. Give its volume in cubic feet.
Divide each dimension in inches by 12 to convert from inches to feet:
feet
feet
feet
Multiply the three to get the volume:
cubic feet
Divide each dimension in inches by 12 to convert from inches to feet:
Multiply the three to get the volume:
Compare your answer with the correct one above
The above depicts a rectangular swimming pool for an apartment. The pool is six feet deep everywhere. What is the volume of the pool in cubic feet?
The above depicts a rectangular swimming pool for an apartment. The pool is six feet deep everywhere. What is the volume of the pool in cubic feet?
The pool can be seen as a rectangular prism with dimensions 50 feet by 35 feet by 6 feet; its volume is
cubic feet.
The pool can be seen as a rectangular prism with dimensions 50 feet by 35 feet by 6 feet; its volume is
Compare your answer with the correct one above
One cubic foot is equal to (about) 7.5 gallons.
The above depicts a rectangular swimming pool for an apartment. The pool is seven feet deep everywhere. How many gallons of water does the pool hold?
One cubic foot is equal to (about) 7.5 gallons.
The above depicts a rectangular swimming pool for an apartment. The pool is seven feet deep everywhere. How many gallons of water does the pool hold?
The pool can be seen as a rectangular prism with dimensions 50 feet by 35 feet by 7 feet; its volume in cubic feet the product of these dimensions, which is
cubic feet.
One cubic foot is equal to about 7.5 gallons, so multiply:
gallons.
The pool can be seen as a rectangular prism with dimensions 50 feet by 35 feet by 7 feet; its volume in cubic feet the product of these dimensions, which is
One cubic foot is equal to about 7.5 gallons, so multiply:
Compare your answer with the correct one above
Which is the greater quantity?
(a) The sidelength of a cube with surface area
(b) The sidelength of a cube with volume
Which is the greater quantity?
(a) The sidelength of a cube with surface area
(b) The sidelength of a cube with volume
(a) A cube has six faces, each a square. Since the surface area of this cube is , each face has one-sixth this area, or ; the sidelength is the square root of this, or .
(b) The volume of a cube is the cube of its sidelength, so we take the cube root of the volume of this cube to get the sidelength:
The cubes have the same sidelength.
(a) A cube has six faces, each a square. Since the surface area of this cube is
(b) The volume of a cube is the cube of its sidelength, so we take the cube root of the volume of this cube to get the sidelength:
The cubes have the same sidelength.
Compare your answer with the correct one above
Which is the greater quantity?
(a) The volume of a rectangular prism with length 60 centimeters, width 30 centimeters, and height 15 centimeters
(b) The volume of a cube with sidelength 300 millimeters
Which is the greater quantity?
(a) The volume of a rectangular prism with length 60 centimeters, width 30 centimeters, and height 15 centimeters
(b) The volume of a cube with sidelength 300 millimeters
(a) The volume of the prism is the product of its length, its width, and its height:
(b) The volume of the cube is the cube of its sidelength. We restate 300 millimeters as 30 centimeters, and cube this:
The volumes are equal.
(a) The volume of the prism is the product of its length, its width, and its height:
(b) The volume of the cube is the cube of its sidelength. We restate 300 millimeters as 30 centimeters, and cube this:
The volumes are equal.
Compare your answer with the correct one above
Give the volume of the box in cubic inches.
Give the volume of the box in cubic inches.
Use the volume formula, substituting :
Use the volume formula, substituting
Compare your answer with the correct one above
Give the volume of the above box in cubic centimeters.
Give the volume of the above box in cubic centimeters.
100 centimeters make one meter, so convert each of the dimensions of the box by multiplying by 100.
centimeters
centimeters
Use the volume formula, substituting :
cubic centimeters
100 centimeters make one meter, so convert each of the dimensions of the box by multiplying by 100.
Use the volume formula, substituting
Compare your answer with the correct one above