All GMAT Math Resources
Example Questions
Example Question #1 :Calculating The Surface Area Of A Cube
What is the surface area of a box that is 3 feet long, 2 feet wide, and 4 feet high?
Example Question #92 :Rectangular Solids & Cylinders
What is the surface area of a cube with side length 4?
Example Question #93 :Rectangular Solids & Cylinders
The surface area of a certain cube is 150 square feet. If the width of the cube is increased by 2 feet, the length decreased by 2 feet and the height increased by 1 foot, what is the new surface area?
The first step to answering this qestion is to determine the original length of the sides of the cube. The surface area of a cube is given by:
Whereis the length of each side. This tells us that for our cube:
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If the width increases by 2, the length decreases by 2 and the height increases by 1:
,,
We now have arectangular prism. The surface area of a rectangular prism is given by:
For our prism:
Example Question #94 :Rectangular Solids & Cylinders
What is the surface area of a cube with a side length of?
Example Question #95 :Rectangular Solids & Cylinders
A cube is inscribed inside a sphere with surface area. Give the volume of the cube.
Each diagonal of the inscribed cube is a diameter of the sphere, so its length is the sphere's diameter, or twice its radius.
The sphere has surface area, so the radius is calculated as follows:
The diameter of the circle - and the length of a diagonal of the cube - is twice this, or 10.
Now, letbe the length of one edge of the cube. By the three-dimensional extension of the Pythagorean Theorem,
立方体的体积是多维数据集,或
Example Question #96 :Rectangular Solids & Cylinders
A sphere of volumeis inscribed inside a cube. Give the surface area of the cube.
The diameter of a sphere is equal to the length of an edge of the cube in which it is inscribed. We can derive the radius using the volume formula:
Twice this, or 12, is the diameter, and, subsequently, the length of an edge of the cube. If,表面面积
Example Question #1 :Calculating The Surface Area Of A Cube
A cube is inscribed inside a sphere of volume. Give the surface area of the cube.
The diameter of a sphere is equal to the length of a diagonal of the cube it circumscribes. We can derive the radius using the volume formula:
Twice this, or 12, is the diameter, and, subsequently, the length of a diagonal of the cube. By an extension of the Pythagorean Theorem, ifis the length of an edge of the cube,
The surface area is six times this:
Example Question #2 :Calculating The Surface Area Of A Cube
Cube A is inscribed inside a sphere, which is inscribed inside Cube B. Give the ratio of the surface area of Cube B to that of Cube A.
Suppose the sphere has diameter.
Then Cube B, the circumscribing cube, has as its edge length the diameter, and its surface area is.
Also, Cube A, the inscribed cube, has this diameter as the length of its diagonal. Ifis the length of an edge, then from the three-dimensional extension of the Pythagorean Theorem,
The surface area is, so
.
The ratio of the surface areas is
The correct choice is.
Example Question #3 :Calculating The Surface Area Of A Cube
The length of one side of a cube is 4 meters. What is the surface area of the cube?
By definition, all sides of a cube are equal in length, so each face is a square, There are six faces on a cube, so its total surface area is six times the area of one of its square faces. If one of its sides is 4 meters, then this will also be the other dimension of one of its square faces, so the total surface area is:
Example Question #4 :Calculating The Surface Area Of A Cube
Find the surface area of a cube whose side length is.
To solve, remember that the equation for surface area of a cube is: