Solid Geometry

Help Questions

Math › Solid Geometry

Questions 1 - 10

1

Find the volume of the following sphere.

Sphere

$288 \pi m^3$

$270 \pi m^3$

$300 \pi m^3$

$312 \pi m^3$

$360 \pi m^3$

Explanation

The formula for the volume of a sphere is:

$V=\frac{4}{3} \pi r^3$

where is the radius of the sphere.

Plugging in our values, we get:

$V=\frac{4}{3} \pi (6m)^3$

$V=\frac{4}{3} \pi 216m^3 = 288 \pi m^3$

2

If the surface area of a cube equals 96, what is the length of one side of the cube?

4

3

6

5

Explanation

The surface area of a cube = 6a2 where a is the length of the side of each edge of the cube. Put another way, since all sides of a cube are equal, a is just the lenght of one side of a cube.

We have 96 = 6a2 → a2 = 16, so that's the area of one face of the cube.

Solving we get √16, so a = 4

3

Find the length of an edge of the following cube:

Length_of_edge

The volume of the cube is $27\ m^3$ .

$3\ m$

$6\ m$

$9\ m$

$12\ m$

$15\ m$

Explanation

The formula for the volume of a cube is

,

where is the length of the edge of a cube.

Plugging in our values, we get:

$27\ m^3 = (e)^3$

$e = 3\ m$

4

What is the surface area of a sphere with a radius of ?

$576\pi$

$144\pi$

$288\pi$

$24\pi$

Explanation

To solve for the surface area of a sphere you must remember the formula:

First, plug the radius into the equation for :

$SA=(4)(12^{2})(\pi)$

Since $(12^{2})=144$ , the surface area is $(4)(144)(\pi)=576\pi$ .

The answer is therefore $576\pi$ .

5

Find the volume of the following triangular prism:

Triangular_prism

$108\sqrt{3}m^3$

$98\sqrt{3}m^3$

$88\sqrt{3}m^3$

$118\sqrt{3}m^3$

$128\sqrt{3}m^3$

Explanation

The formula for the volume of an equilateral, triangular prism is:

$V = \left(\frac{s^2\sqrt{3}}{4}\right)(h)$

Where is the length of the triangle side and is the length of the height.

Plugging in our values, we get:

$V = \left(\frac{(6m)^2\sqrt{3}}{4}\right)(12m)$

$V=108\sqrt{3}m^3$

6

A cube has a side length of meters. What is the volume of the cube?

$8\ \textup{m}^{3}$

$6\ \textup{m}^{3}$

$4\ \textup{m}^{3}$

$2\ \textup{m}^{3}$

$16\ \textup{m}^{3}$

Explanation

The formula for the volume of a cube is:

$Volume = (side)^{3}$

Since the length of one side is meters, the volume of the cube is:

$2^{3 } = 8$ meters cubed.

7

The volume of a sphere is $2 8 8 \pi$ . What is the diameter?

Explanation

To find the diameter of the sphere, we need to find the radius.

The volume of a sphere is $V=\frac{4}{3}\pi r^3$ .

Plug in our given values.

$2 88\pi=\frac{4}{3}\pi r^3$

Notice that the $\pi$ 's cancel out.

$288=\frac{4}{3}r^3$

$\frac{3}{4}*288=r^3$

$\sqrt[3]{216}=\sqrt[3]{r^3}$

The diameter is twice the radius, so .

8

What is the surface area of a sphere with a radius of ?

$576\pi$

$144\pi$

$288\pi$

$24\pi$

Explanation

To solve for the surface area of a sphere you must remember the formula:

First, plug the radius into the equation for :

$SA=(4)(12^{2})(\pi)$

Since $(12^{2})=144$ , the surface area is $(4)(144)(\pi)=576\pi$ .

The answer is therefore $576\pi$ .

9

Find the volume of the following sphere.

Sphere

$288 \pi m^3$

$270 \pi m^3$

$300 \pi m^3$

$312 \pi m^3$

$360 \pi m^3$

Explanation

The formula for the volume of a sphere is:

$V=\frac{4}{3} \pi r^3$

where is the radius of the sphere.

Plugging in our values, we get:

$V=\frac{4}{3} \pi (6m)^3$

$V=\frac{4}{3} \pi 216m^3 = 288 \pi m^3$

10

What is the diameter of a sphere with a volume of $36\pi$ ?

Explanation

The volume of a sphere is determined by the following equation:

$V=\frac{4}{3}\pi r^3$

$36\pi=\frac{4}{3}\pi r^3$

$(\frac{3}{4})36\pi=(\frac{3}{4})(\frac{4}{3})\pi r^3$

$\frac{27\pi}{\pi}=\frac{\pi r^3}{\pi}$

$\sqrt[3]{27}=\sqrt[3]{r^3}$

Page 1 of 48

Return to subject