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Intermediate Geometry : Spheres

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Example Questions

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

If the volume of a sphere is $1\:unit$ , what is the sphere's exact radius?

Possible Answers:

$\sqrt{\frac{1}{\pi}}\:units$

$\sqrt{\frac{2}{3\pi}}\:units$

$\sqrt[3]{\frac{4\pi}{3}}\:units$

$\sqrt{\pi}\:units$

$\sqrt[3]{\frac{3}{4\pi}}\:units$

Correct answer:

$\sqrt[3]{\frac{3}{4\pi}}\:units$

Explanation:

Write the formula for the volume of a sphere:

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

Plug in the given volume and solve for the radius, .

$1=\frac{4}{3}\pi r^3$

Start by multiplying each side of the equation by $\frac{3}{4}$ :

$\frac{3}{4}\cdot1=\frac{4}{3}\pi r^3\cdot\frac{3}{4}$

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

Now, divide each side of the equation by $\pi$ :

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

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

Finally, take the cubed root of each side of the equation:

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

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Example Question #5 : How To Find The Radius Of A Sphere

Given the volume of a sphere is $\frac{4}{3}\pi\:cm^3$ , what is the radius?

Possible Answers:

$\frac{\sqrt2}{3}\:cm$

$\frac{4}{3}\:cm$

$1\:cm$

$\frac{1}{2}\:cm$

$\frac{1}{4}\:cm$

Correct answer:

$1\:cm$

Explanation:

The equation for the volume of a sphere is:

$V=\frac{4}{3}\pi r^3$ , where is the length of the sphere's radius.

Plug in the given volume and solve for to calculate the sphere's radius:

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

1=r^3

r=1

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

If the volume of a sphere is $4\:m^3$ , what is the radius of the sphere?

Possible Answers:

$\sqrt[3]{\frac{3}{\pi}}\:m$

$\sqrt[3]{\frac{1}{3\pi}}\:m$

$\sqrt[3]{\frac{16}{3\pi}}\:m$

$\sqrt[3]{3\pi}\:m$

$\sqrt[3]{\frac{3}{\pi}}\:m$

Correct answer:

$\sqrt[3]{\frac{3}{\pi}}\:m$

Explanation:

The formula for the volume of a sphere is:

$V=\frac{4}{3}\pi r^3$ , where is the sphere's radius.

Plug in the volume and solve for , the sphere's radius:

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

$3=\pi r^3$

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

$r=\sqrt[3]{\frac{3}{\pi}}\:m$

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

Find the radius of a sphere if the surface area is $8\pi\:cm^2$ .

Possible Answers:

$2\:cm$

$\sqrt{2}\:cm$

$\sqrt{\frac{1}{2}}\:cm$

$\frac{1}{2}\:cm$

$2\sqrt 2\:cm$

Correct answer:

$\sqrt{2}\:cm$

Explanation:

The formula for the surface area of a sphere is:

$SA=4\pi r^2$

Substitute the given value for the sphere's surface area into the equation and solve for to find the radius:

$8\pi=4\pi r^2$

2=r^2

$r=\sqrt2\:cm$

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

Find the radius of a sphere if its surface area is $8\:in^2$ .

Possible Answers:

$\sqrt\frac{\pi}{2}\:in$

$\sqrt\frac{2}{\pi}\:in$

$\sqrt\frac{\pi}{8}\:in$

$\sqrt\frac{8}{\pi}\:in$

$\sqrt2\:in$

Correct answer:

$\sqrt\frac{2}{\pi}\:in$

Explanation:

The surface area formula for a sphere is:

$A=4\pi r^2$ , where is the sphere's radius.

Substitute the given value for the sphere's area into the equation and solve for to find the radius:

$8=4\pi r^2$

$\frac{2}{\pi}= r^2$

$r=\sqrt{\frac{2}{\pi}}\:in$

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Intermediate Geometry : Spheres

Study concepts, example questions & explanations for Intermediate Geometry

All Intermediate Geometry Resources

Example Questions

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

Example Question #5 : How To Find The Radius Of A Sphere

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

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

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

All Intermediate Geometry Resources

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