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High School Math : Spheres

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Example Question #6 : How To Find The Surface Area Of A Sphere

Given that the radius of a sphere is 3, find the surface area.

Possible Answers:

$4\pi$

$36\pi$

$12\pi$

$9\pi$

$16\pi$

Correct answer:

$36\pi$

Explanation:

The standard equation to find the area of a sphere is

$SA=4\pi r^2$

where denotes the radius. Plug in the given radius to find the surface area.

$SA=4\pi (3)^2=4\cdot 9\cdot \pi =36\pi$

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Example Question #7 : How To Find The Surface Area Of A Sphere

Find the surface area of the following sphere.

Sphere

Possible Answers:

$145 \pi m^2$

$160 \pi m^2$

$124 \pi m^2$

$130 \pi m^2$

$144 \pi m^2$

Correct answer:

$144 \pi m^2$

Explanation:

The formula for the surface area of a sphere is:

$SA = 4 \pi r^2$

where is the radius of the sphere.

Plugging in our values, we get:

$SA = 4 \pi (6m)^2$

$SA = 4 \pi (36m) = 144 \pi m^2$

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Example Question #8 : How To Find The Surface Area Of A Sphere

Find the surface area of the following sphere.

Sphere

Possible Answers:

$304 \pi m^2$

$324 \pi m^2$

$314 \pi m^2$

$334 \pi m^2$

$344 \pi m^2$

Correct answer:

$324 \pi m^2$

Explanation:

The formula for the surface area of a sphere is:

$SA = 4 \pi (r^2)$

Where is the radius of the sphere

Plugging in our values, we get:

$SA = 4 \pi (9m)^2$

$SA = 324 \pi m^2$

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Example Question #1 : How To Find The Surface Area Of A Sphere

What is the surface area of a composite figure of a cone and a sphere, both with a radius of 5 cm, if the height of the cone is 12 cm? Consider an ice cream cone as an example of the composite figure, where half of the sphere is above the edge of the cone.

Possible Answers:

$115\pi\ cm^2$

$50\pi\ cm^2$

$65\pi\ cm^2$

$125\pi\ cm^2$

$165\pi\ cm^2$

Correct answer:

$115\pi\ cm^2$

Explanation:

Calculate the slant height height of the cone using the Pythagorean Theorem. The height will be the height of the cone, the base will be the radius, and the hypotenuse will be the slant height.

s^2=r^2+h^2

$s=\sqrt{169}=13$

The surface area of the cone (excluding the base) is given by the formula $A=\pi rs$ . Plug in our values to solve.

$A_{cone}=\pi(5)(13)=65\pi\ cm^2$

The surface area of a sphere is given by $A=4\pi r^2$ but we only need half of the sphere, so the area of a hemisphere is $A=2\pi r^2$ .

$A_{hemisphere}=2\pi(5)^2=50\pi\ cm^2$

So the total surface area of the composite figure is $65\pi\ cm^2+50\pi\ cm^2=115\pi\ cm^2$ .

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Example Question #8 : How To Find The Surface Area Of A Sphere

What is the surface area of a hemisphere with a diameter of $4\ cm$ ?

Possible Answers:

$16\pi \ cm^{2}$

$8\pi \ cm^{2}$

$12\pi \ cm^{2}$

$20\pi \ cm^{2}$

$18\pi \ cm^{2}$

Correct answer:

$12\pi \ cm^{2}$

Explanation:

A hemisphere is half of a sphere. The surface area is broken into two parts: the spherical part and the circular base.

The surface area of a sphere is given by $SA = 4\pi r^{2}$ .

So the surface area of the spherical part of a hemisphere is $SA = 2\pi r^{2}$ .

The area of the circular base is given by $A = \pi r^{2}$ . The radius to use is half the diameter, or 2 cm.

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Example Question #21 : Spheres

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

Possible Answers:

576

$144\pi$

$288\pi$

$24\pi$

$576\pi$

Correct answer:

$576\pi$

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 $576\pi$ .

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Example Question #1 : How To Find The Diameter Of A Sphere

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

Possible Answers:

Correct answer:

Explanation:

To find the diameter of a sphere we must use the equation for the volume of a sphere to find the radius which is half of the diameter.

The equation is

First we enter the volume into the equation yielding $36\pi=(\frac{4}{3})(\pi)(r^{3})$

We then divide each side by to get $36=(\frac{4}{3})(r^{3})$

We then multiply each side by to get $27=r^{3}$

We then take the cubic root of each side to solve for the radius $\sqrt[3]{27}=\sqrt[3]{r^{3}}$

The radius is r=3

We then multiply the radius by 2 to find the diameter 3*2=6

The answer for the diameter is .

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Example Question #2 : How To Find The Diameter Of A Sphere

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

Possible Answers:

14.7

29.4

Correct answer:

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.

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

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

216=r^3

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

6= r

The diameter is twice the radius, so d=2r .

d=2(6)

d=12

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Example Question #3 : How To Find The Diameter Of A Sphere

If the surface area of a sphere is $64\pi$ , find the diameter of this sphere.

Possible Answers:

$4\pi$

$4\sqrt{\pi }$

$\sqrt{8\pi }$

Correct answer:

Explanation:

The standard equation to find the surface area of a sphere is

$SA=4\pi r^2$ where denotes the radius. Rearrange this equation in terms of :

$r=\sqrt{\frac{SA}{4\pi }}$

Substitute the given surface area into this equation and solve for the radius and then double the radius to get the diameter:

$r=\sqrt{\frac{64\Pi }{4\Pi }}=\sqrt{16}=4$

$diameter=2\cdot r=2\cdot 4=8$

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Example Question #4 : How To Find The Diameter Of A Sphere

Given that the volume of a sphere is $4\pi$ , find the diameter.

Possible Answers:

$2\pi \sqrt[3]{3}$

$2\sqrt[3]{3}$

$2\sqrt[3]{4}$

$2\sqrt[3]{4\pi }$

$2\sqrt[3]{3\pi }$

Correct answer:

$2\sqrt[3]{3}$

Explanation:

The standard equation to find the volume of a sphere is

$V=\frac{4}{3}\pi r^3$ where denotes the radius. Rearrange this equation in terms of :

$r=\sqrt[3]{\frac{3V}{4\pi }}$

Substitute the given volume into this equation and solve for the radius. Double the radius to find the diameter:

$r=\sqrt[3]{\frac{3V}{4\pi }}=\sqrt[3]{\frac{3\cdot 4\pi }{4\pi }}=\sqrt[3]{\frac{12\pi }{4\pi }}=\sqrt[3]{3 }$

$diameter=2\cdot r=2\sqrt[3]{3}$

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High School Math : Spheres

Study concepts, example questions & explanations for High School Math

All High School Math Resources

Example Questions

Example Question #6 : How To Find The Surface Area Of A Sphere

Example Question #7 : How To Find The Surface Area Of A Sphere

Example Question #8 : How To Find The Surface Area Of A Sphere

Example Question #1 : How To Find The Surface Area Of A Sphere

Example Question #8 : How To Find The Surface Area Of A Sphere

Example Question #21 : Spheres

Example Question #1 : How To Find The Diameter Of A Sphere

Example Question #2 : How To Find The Diameter Of A Sphere

Example Question #3 : How To Find The Diameter Of A Sphere

Example Question #4 : How To Find The Diameter Of A Sphere

All High School Math Resources

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