Spheres - HiSET

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Question

The surface area of a sphere is equal to $100 \pi$ . Give the volume of the sphere.

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Answer

The surface area of a sphere can be calculated using the formula

$A = 4 \pi $r^{2}$$

Solving for :

Set $A = 100 \pi$ and divide both sides by $4 \pi$ :

$4 \pi $r^{2}$ = 100 \pi$

$\frac{4 \pi $r^{2}$$}{4 \pi} = $\frac{100 \pi}{4 \pi}$

Take the square root of both sides:

$r = $\sqrt{25}$ = 5$

Set in the volume formula:

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

$V= $\frac{4}{3}$ \pi \left(5 \right $)^{3}$ = $\frac{4}{3}$ \pi \left(125 \right) = $\frac{500}{3}$\pi$ ,

the correct response.

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Question

A sphere has surface area $64 \pi$ . Give its volume.

Tap to reveal answer

Answer

The surface area of a sphere, given its radius , is equal to

$A= 4 \pi $r^{2}$$

Substitute $64\pi$ for and solve for :

$4 \pi $r^{2}$ = 64 \pi$

Divide by $4 \pi$ :

$\frac{4 \pi $r^{2}$$}{4 \pi} = $\frac{64 \pi}{4 \pi}$

Extract the square root:

Substitute for in the volume formula:

$V = $\frac{4}{3}$ \pi $r^{3}$= $\frac{4}{3}$ \pi \cdot $4^{3}$ =\frac{4}{3}$ \pi \cdot 64 = $\frac{256}{3}$\pi$ ,

the correct response.

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Question

The surface area of a sphere is equal to $100 \pi$ . Give the volume of the sphere.

Tap to reveal answer

Answer

The surface area of a sphere can be calculated using the formula

$A = 4 \pi $r^{2}$$

Solving for :

Set $A = 100 \pi$ and divide both sides by $4 \pi$ :

$4 \pi $r^{2}$ = 100 \pi$

$\frac{4 \pi $r^{2}$$}{4 \pi} = $\frac{100 \pi}{4 \pi}$

Take the square root of both sides:

$r = $\sqrt{25}$ = 5$

Set in the volume formula:

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

$V= $\frac{4}{3}$ \pi \left(5 \right $)^{3}$ = $\frac{4}{3}$ \pi \left(125 \right) = $\frac{500}{3}$\pi$ ,

the correct response.

← Didn't Know|Knew It →

Question

A sphere has surface area $64 \pi$ . Give its volume.

Tap to reveal answer

Answer

The surface area of a sphere, given its radius , is equal to

$A= 4 \pi $r^{2}$$

Substitute $64\pi$ for and solve for :

$4 \pi $r^{2}$ = 64 \pi$

Divide by $4 \pi$ :

$\frac{4 \pi $r^{2}$$}{4 \pi} = $\frac{64 \pi}{4 \pi}$

Extract the square root:

Substitute for in the volume formula:

$V = $\frac{4}{3}$ \pi $r^{3}$= $\frac{4}{3}$ \pi \cdot $4^{3}$ =\frac{4}{3}$ \pi \cdot 64 = $\frac{256}{3}$\pi$ ,

the correct response.

← Didn't Know|Knew It →

Question

The surface area of a sphere is equal to $100 \pi$ . Give the volume of the sphere.

Tap to reveal answer

Answer

The surface area of a sphere can be calculated using the formula

$A = 4 \pi $r^{2}$$

Solving for :

Set $A = 100 \pi$ and divide both sides by $4 \pi$ :

$4 \pi $r^{2}$ = 100 \pi$

$\frac{4 \pi $r^{2}$$}{4 \pi} = $\frac{100 \pi}{4 \pi}$

Take the square root of both sides:

$r = $\sqrt{25}$ = 5$

Set in the volume formula:

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

$V= $\frac{4}{3}$ \pi \left(5 \right $)^{3}$ = $\frac{4}{3}$ \pi \left(125 \right) = $\frac{500}{3}$\pi$ ,

the correct response.

← Didn't Know|Knew It →

Question

A sphere has surface area $64 \pi$ . Give its volume.

Tap to reveal answer

Answer

The surface area of a sphere, given its radius , is equal to

$A= 4 \pi $r^{2}$$

Substitute $64\pi$ for and solve for :

$4 \pi $r^{2}$ = 64 \pi$

Divide by $4 \pi$ :

$\frac{4 \pi $r^{2}$$}{4 \pi} = $\frac{64 \pi}{4 \pi}$

Extract the square root:

Substitute for in the volume formula:

$V = $\frac{4}{3}$ \pi $r^{3}$= $\frac{4}{3}$ \pi \cdot $4^{3}$ =\frac{4}{3}$ \pi \cdot 64 = $\frac{256}{3}$\pi$ ,

the correct response.

← Didn't Know|Knew It →

Question

The surface area of a sphere is equal to $100 \pi$ . Give the volume of the sphere.

Tap to reveal answer

Answer

The surface area of a sphere can be calculated using the formula

$A = 4 \pi $r^{2}$$

Solving for :

Set $A = 100 \pi$ and divide both sides by $4 \pi$ :

$4 \pi $r^{2}$ = 100 \pi$

$\frac{4 \pi $r^{2}$$}{4 \pi} = $\frac{100 \pi}{4 \pi}$

Take the square root of both sides:

$r = $\sqrt{25}$ = 5$

Set in the volume formula:

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

$V= $\frac{4}{3}$ \pi \left(5 \right $)^{3}$ = $\frac{4}{3}$ \pi \left(125 \right) = $\frac{500}{3}$\pi$ ,

the correct response.

← Didn't Know|Knew It →

Question

A sphere has surface area $64 \pi$ . Give its volume.

Tap to reveal answer

Answer

The surface area of a sphere, given its radius , is equal to

$A= 4 \pi $r^{2}$$

Substitute $64\pi$ for and solve for :

$4 \pi $r^{2}$ = 64 \pi$

Divide by $4 \pi$ :

$\frac{4 \pi $r^{2}$$}{4 \pi} = $\frac{64 \pi}{4 \pi}$

Extract the square root:

Substitute for in the volume formula:

$V = $\frac{4}{3}$ \pi $r^{3}$= $\frac{4}{3}$ \pi \cdot $4^{3}$ =\frac{4}{3}$ \pi \cdot 64 = $\frac{256}{3}$\pi$ ,

the correct response.

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