Question

What is the volume of a sphere with a surface area of 25pi

Answer 1

To calculate the volume of a sphere with a given surface area of 25π, first find the radius using the surface area formula and then use this radius to calculate the volume. The volume is approximately 65.45π cm³.

Step-by-step explanation:

Calculating the Volume of a Sphere from its Surface Area

To find the volume of a sphere when given the surface area, you can use the formula for surface area SA = 4πr² to find the radius and then insert that radius into the formula for volume V = 4/3πr³. Given the surface area SA = 25π, we can solve for the radius r:

25π = 4πr²

Divide both sides by 4π:

(25π) / (4π) = r²

6.25 = r²

Take the square root:

√6.25 = r

2.5 = r

Now we can use the value of r to find the volume of the sphere:

V = 4/3π(2.5)³

Calculate the volume:

V = 4/3π(15.625)

V = 4/3π(15.625) = Π65.45π cm³

Therefore, the volume of the sphere with a surface area of 25π is approximately 65.45π cm³.

Answer 2

(125/6)π units³

Step-by-step explanation:

The formula for the surface area of a sphere is A = 4πr². Solving this for r² yields:

A

r² = ------

4π

and in this case r² is:

25π

r² = ---------, or 25/4 units²

4π

Thus, the radius, r, is 5/2 units.

The volume of a sphere of radius r is V = (4/3)πr³ units³

Here, that volume is V = (4/3)π(5/2)³ units³

4π 125 units³

= ------ · ------------------ = (125/6)π units³

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