Question

find (a) the volume and (b) the surface area of the sphere. use 3.14 as an approximation for π. (a) find the volume of the solid. volume = (round to the nearest hundredth as needed.) (b) find the surface area of the solid. surface area = (round to the nearest hundredth as needed.)

Explanation:

Step1: Find the radius

The diameter $d = 42$ ft, so the radius $r=\frac{d}{2}=\frac{42}{2}=21$ ft.

Step2: Calculate the volume of the sphere

The volume formula of a sphere is $V = \frac{4}{3}\pi r^{3}$. Substitute $r = 21$ and $\pi=3.14$ into the formula:
$V=\frac{4}{3}\times3.14\times21^{3}=\frac{4}{3}\times3.14\times9261 = 4\times3.14\times3087=38772.72$ cubic - feet.

Step3: Calculate the surface - area of the sphere

The surface - area formula of a sphere is $A = 4\pi r^{2}$. Substitute $r = 21$ and $\pi = 3.14$ into the formula:
$A=4\times3.14\times21^{2}=4\times3.14\times441 = 5538.96$ square - feet.

Answer:

(a) Volume = $38772.72$ cubic feet
(b) Surface Area = $5538.96$ square feet