How to find the radius of a sphere - Geometry

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Question

If the volume of a sphere is $120\ ft^{3}$ , what is the approximate length of its diameter?

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

Answer

The correct answer is 6.12 ft.

Plug the value of into the equation so that

$120=\frac{4}{3}\pi r^{3}$

Multiply both sides by 3 to get

$360=4\pi r^{3}$

Then divide both sides by $4\pi$ to get

$28.65=r^{3}$

Then take the 3rd root of both sides to get 3.06 ft for the radius. Finally, you have to multiply by 2 on both sides to get the diameter. Thus

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Question

The volume of a sphere is . What is its radius?

Answer

The formula for the volume of a sphere is: $\frac{4}{3} \pi r^3 = V$

The only given information in the problem is the sphere's final volume. If the volume is , the formula for volume can be used to calculate the sphere's radius.

In this case, , the radius, is the only unknown variable that needs to be solved for.

$\frac{4}{3} \pi r^3 = 57$

$\frac{3}{4}\cdot \frac{1}{\pi}\cdot\frac{4}{3} \pi r^3 = 57 \cdot\frac{3}{4}\cdot \frac{1}{\pi}$

$r^3 = \frac{171}{4\cdot \pi}$

$\sqrt[3]{r^3}=\sqrt[3]{\frac{171}{4\cdot \pi}} = \sqrt[3]{13.608}$

$r=\sqrt[3]{13.608}$

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Question

The area of a sphere is . What is its radius?

Answer

The only information given is the area of .

This problem may be approached "backwards," where the area formula for a sphere can be used to solve for the radius. This is possible because the formula for area is $Area = 4 \cdot \pi \cdot r^2$ , where (the radius) is what we're looking for. After is substituted in for the area, the goal is to solve for by getting it by itself on one side of the equals sign.

$87=4 \cdot \pi \cdot r^2$

$\frac{87}{4\cdot\pi}=\frac{4 \cdot \pi \cdot r^2}{4\cdot\pi}$

$\sqrt{\frac{87}{4 \cdot \pi}} = \sqrt{r^2} = r$

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Question

If the volume of a sphere is , what is the sphere's exact radius?

Answer

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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Question

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

Answer

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:

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

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Question

If the volume of a sphere is , what is the radius of the sphere?

Answer

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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Question

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

Answer

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:

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

$r=\sqrt2:cm$

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Question

Find the radius of a sphere if its surface area is .

Answer

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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Question

If the volume of a sphere is $120\ ft^{3}$ , what is the approximate length of its diameter?

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

Answer

The correct answer is 6.12 ft.

Plug the value of into the equation so that

$120=\frac{4}{3}\pi r^{3}$

Multiply both sides by 3 to get

$360=4\pi r^{3}$

Then divide both sides by $4\pi$ to get

$28.65=r^{3}$

Then take the 3rd root of both sides to get 3.06 ft for the radius. Finally, you have to multiply by 2 on both sides to get the diameter. Thus

Compare your answer with the correct one above

Question

The volume of a sphere is . What is its radius?

Answer

The formula for the volume of a sphere is: $\frac{4}{3} \pi r^3 = V$

The only given information in the problem is the sphere's final volume. If the volume is , the formula for volume can be used to calculate the sphere's radius.

In this case, , the radius, is the only unknown variable that needs to be solved for.

$\frac{4}{3} \pi r^3 = 57$

$\frac{3}{4}\cdot \frac{1}{\pi}\cdot\frac{4}{3} \pi r^3 = 57 \cdot\frac{3}{4}\cdot \frac{1}{\pi}$

$r^3 = \frac{171}{4\cdot \pi}$

$\sqrt[3]{r^3}=\sqrt[3]{\frac{171}{4\cdot \pi}} = \sqrt[3]{13.608}$

$r=\sqrt[3]{13.608}$

Compare your answer with the correct one above

Question

The area of a sphere is . What is its radius?

Answer

The only information given is the area of .

This problem may be approached "backwards," where the area formula for a sphere can be used to solve for the radius. This is possible because the formula for area is $Area = 4 \cdot \pi \cdot r^2$ , where (the radius) is what we're looking for. After is substituted in for the area, the goal is to solve for by getting it by itself on one side of the equals sign.

$87=4 \cdot \pi \cdot r^2$

$\frac{87}{4\cdot\pi}=\frac{4 \cdot \pi \cdot r^2}{4\cdot\pi}$

$\sqrt{\frac{87}{4 \cdot \pi}} = \sqrt{r^2} = r$

Compare your answer with the correct one above

Question

If the volume of a sphere is , what is the sphere's exact radius?

Answer

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:

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

Compare your answer with the correct one above

Question

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

Answer

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:

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

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Question

If the volume of a sphere is , what is the radius of the sphere?

Answer

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:

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

$3=\pi r^3$

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

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

Compare your answer with the correct one above

Question

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

Answer

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:

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

$r=\sqrt2:cm$

Compare your answer with the correct one above

Question

Find the radius of a sphere if its surface area is .

Answer

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:

$8=4\pi r^2$

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

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

Compare your answer with the correct one above

Question

If the volume of a sphere is $120\ ft^{3}$ , what is the approximate length of its diameter?

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

Answer

The correct answer is 6.12 ft.

Plug the value of into the equation so that

$120=\frac{4}{3}\pi r^{3}$

Multiply both sides by 3 to get

$360=4\pi r^{3}$

Then divide both sides by $4\pi$ to get

$28.65=r^{3}$

Then take the 3rd root of both sides to get 3.06 ft for the radius. Finally, you have to multiply by 2 on both sides to get the diameter. Thus

Compare your answer with the correct one above

Question

The volume of a sphere is . What is its radius?

Answer

The formula for the volume of a sphere is: $\frac{4}{3} \pi r^3 = V$

The only given information in the problem is the sphere's final volume. If the volume is , the formula for volume can be used to calculate the sphere's radius.

In this case, , the radius, is the only unknown variable that needs to be solved for.

$\frac{4}{3} \pi r^3 = 57$

$\frac{3}{4}\cdot \frac{1}{\pi}\cdot\frac{4}{3} \pi r^3 = 57 \cdot\frac{3}{4}\cdot \frac{1}{\pi}$

$r^3 = \frac{171}{4\cdot \pi}$

$\sqrt[3]{r^3}=\sqrt[3]{\frac{171}{4\cdot \pi}} = \sqrt[3]{13.608}$

$r=\sqrt[3]{13.608}$

Compare your answer with the correct one above

Question

The area of a sphere is . What is its radius?

Answer

The only information given is the area of .

This problem may be approached "backwards," where the area formula for a sphere can be used to solve for the radius. This is possible because the formula for area is $Area = 4 \cdot \pi \cdot r^2$ , where (the radius) is what we're looking for. After is substituted in for the area, the goal is to solve for by getting it by itself on one side of the equals sign.

$87=4 \cdot \pi \cdot r^2$

$\frac{87}{4\cdot\pi}=\frac{4 \cdot \pi \cdot r^2}{4\cdot\pi}$

$\sqrt{\frac{87}{4 \cdot \pi}} = \sqrt{r^2} = r$

Compare your answer with the correct one above

Question

If the volume of a sphere is , what is the sphere's exact radius?

Answer

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:

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

Compare your answer with the correct one above

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