Question

the surface area of a sphere is 1,017.36 square inches.what is the volume of the sphere? use 3.14 for pi

Answer 1

Answer:

Area = 254.34 inches ³

Step-by-step explanation:

The formula to find the surface area of a sphere is:

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

To find the volume of the sphere, we first need to figure out the radius ($r$) of the sphere. We can accomplish this by reversing the formula that was used to find the surface area. $(1017.36 in^{2})$

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

$1017.36 = 4\pi r^{2}$

Divide both sides by pi ($3.14$).

$1017.36 = 4\pi r^{2}$

$324 = 4 r^{2}$

Divide both sides by 4.

$324 = 4 r^{2}$

$81 = r^{2}$

Find the square root of both sides.

$81 = r^{2}$

$\sqrt{81} = r$

radius = 9

Insert the value of the radius into the formula for finding the volume of a sphere. $(A=\pi r^{2})$

$(A=\pi r^{2})$

$A=\pi (9)^{2}$

$A=\pi (81)$

$A = 254.34$

Area = 254.34 inches ³

~Hope this helps!~