Rectangular Solids & Cylinders

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GMAT Quantitative › Rectangular Solids & Cylinders

Questions 1 - 10

is a cube and face has an area of . What is the length of diagonal of the cube ?

$3\sqrt{3}$

$2\sqrt{3}$

$3\sqrt{2}$

Explanation

To find the diagonal of a cube we can apply the formula $d=e\sqrt{3}$ , where is the length of the diagonal and where is the length of an edge of the cube.

Since we are given an area of a face of the cube, we can find the length of an edge simply by taking its square root.

$9=s^2 \rightarrow \sqrt 9 =s \rightarrow 3=s$

Here the length of an edge is 3.

Thefore the final andwer is $d=e\sqrt3=3\sqrt{3}$ .

Find the volume of a cylinder whose height is and radius is .

$32\pi$

$16\pi$

$\24\pi$

$8\pi$

Explanation

To find the volume of a cylinder, you must use the following equation:

$V=\pi{r^2}h$

Thus,

$V=\pi(2^2)(8)=32\pi$

Find the volume of a cylinder whose height is and radius is .

$32\pi$

$16\pi$

$\24\pi$

$8\pi$

Explanation

To find the volume of a cylinder, you must use the following equation:

$V=\pi{r^2}h$

Thus,

$V=\pi(2^2)(8)=32\pi$

is a cube and face has an area of . What is the length of diagonal of the cube ?

$3\sqrt{3}$

$2\sqrt{3}$

$3\sqrt{2}$

Explanation

To find the diagonal of a cube we can apply the formula $d=e\sqrt{3}$ , where is the length of the diagonal and where is the length of an edge of the cube.

Since we are given an area of a face of the cube, we can find the length of an edge simply by taking its square root.

$9=s^2 \rightarrow \sqrt 9 =s \rightarrow 3=s$

Here the length of an edge is 3.

Thefore the final andwer is $d=e\sqrt3=3\sqrt{3}$ .

Find the surface area of a cylinder whose height is and radius is .

$54\pi$

$18\pi$

$27\pi$

$45\pi$

Explanation

To find the surface area of a cylinder, you must use the following equation.

$SA=2\pi{r}h+2\pi{r^2}$

Thus,

$SA=2\pi(3)(6)+2\pi(3^2)=54\pi$

Jenny wants to make a cube out of sheet metal. What is the length of one side of the cube?

I) The cube will require square inches of material.

II) The cube will hold cubic inches.

Either statement is sufficient to answer the question.

Both statements are needed to answer the question.

Neither statement is sufficient to answer the question. More information is needed.

Statement I is sufficient to answer the question, but statement II is not sufficient to answer the question.

Statement II is sufficient to answer the question, but statement I is not sufficient to answer the question.

Explanation

The length of an edge of a cube can be used to find either volume or surface area, and vice versa.

I) Gives us the surface area thus, we are able to calculate the length of an edge using the formula,

$SA=6\cdot s^2$

$294=6s^2 \rightarrow 49=s^2 \rightarrow 7=s$ .

II) Gives us the volume thus, we are able to calculate the length of an edge using the formula,

$343=s^3 \rightarrow 7=s$

Either can be used to find the side length.

An aquarium is shaped like a perfect cube; the area of each glass face is square meters. If it is filled to the recommended capacity, then how much water will it contain?

Note: cubic meter liters.

$12,500\textup{ L}$

$15,625\textup{ L}$

$8,000\textup{ L}$

$10,000\textup{ L}$

The correct answer is not given among the other choices.

Explanation

A perfect cube has square faces; if a face has area 6.25 square meters, then each side of each face measures the square root of this, or 2.5 meters. The volume of the tank is the cube of this, or

$2.5^{3} = 15.625$ cubic meters.