SSAT Upper Level Quantitative › How to find the volume of a cube
Find the volume of a cube with a side length of .
Write the formula for the volume of a cube.
The correct answer is .
The length of a diagonal of a cube is . Give the volume of the cube.
Let be the length of one edge of the cube. By the three-dimensional extension of the Pythagorean Theorem,
Cube the sidelength to get the volume:
The length of a diagonal of one face of a cube is . Give the volume of the cube.
The correct answer is not among the other responses.
A diagonal of a square has length times that of a side, so each side of each square face of the cube has length
. Cube this to get the volume:
The distance from one vertex of a cube to its opposite vertex is one foot. Give the volume of the cube in inches.
Since we are looking at inches, we will look at one foot as twelve inches.
Let be the length of one edge of the cube. By the three-dimensional extension of the Pythagorean Theorem,
inches.
Cube this sidelength to get the volume:
cubic inches.
A cheese seller has a 2 foot x 2 foot x 2 foot block of gouda and she wants to cut it into smaller gouda cubes that are 1.5 inches on a side. How many cubes can she cut?
First we need to determine how many of the small cubes of gouda would fit along one dimension of the large cheese block. One edge of the large block is 24 inches, so 16 smaller cubes would fit along the edge. Now we simply cube this one dimension to see how many cubes fit within the whole cube.
.
The distance from one vertex of a perfectly cubic aquarium to its opposite vertex is meters. Give the volume of the aquarium in liters.
cubic meter =
liters.
Let be the length of one edge of the cube. By the three-dimensional extension of the Pythagorean Theorem,
meters.
Cube this sidelength to get the volume:
cubic meters.
To convert this to liters, multiply by 1,000:
liters.
An aquarium is shaped like a perfect cube; the area of each glass face is 1.44 square meters. If it is filled to the recommended 90% capacity, then, to the nearest hundred liters, how much water will it contain?
Note: 1 cubic meter = 1,000 liters.
A perfect cube has square faces; if a face has area 1.44 square meters, then each side of each face measures the square root of this, or 1.2 meters. The volume of the tank is the cube of this, or
cubic meters.
Its capacity in liters is liters.
90% of this is
liters.
This rounds to 1,600 liters, the correct response.
A cube has six square faces, each with area 64 square inches. Using the conversion factor 1 inch = 2.5 centimeters, give the volume of this cube in cubic centimeters, rounding to the nearest whole number.
8,000 cubic centimeters
800 cubic centimeters
2,000 cubic centimeters
400 cubic centimeters
4,000 cubic centimeters
The volume of a cube is the cube of its sidelength, which is also the sidelength of each square face. This sidelength is the square root of the area 64:
inches.
Multiply this by 2.5 to get the sidelength in centimeters:
centimeters.
The cube of this is
cubic centimeters
The distance from one vertex of a cube to its opposite vertex is . Give the volume of the cube.
Let be the length of one edge of the cube. By the three-dimensional extension of the Pythagorean Theorem,
Cube this sidelength to get the volume:
The length of a diagonal of one face of a cube is 10. Give the volume of the cube.
Since a diagonal of a square face of the cube is 10, each side of each square has length times this, or
.
Cube this to get the volume of the cube:
.