Question

the circumference of a cross section of a sphere is 12.56 in. (remember c = πd) find the volume of the sphere. use 3.14 for pi and round to the nearest tenth.

a. 10.7 in³
b. 33.5 in³
c. 85.3 in³
d. 267.9 in³

Explanation:

Step1: Find the diameter of the cross - section

Given $C = \pi d$ and $C=12.56$ in, $\pi = 3.14$. Then $d=\frac{C}{\pi}=\frac{12.56}{3.14}=4$ in.

Step2: Find the radius of the sphere

Since the diameter of the cross - section is equal to the diameter of the sphere, the radius $r=\frac{d}{2}=\frac{4}{2} = 2$ in.

Step3: Calculate the volume of the sphere

The volume formula of a sphere is $V=\frac{4}{3}\pi r^{3}$. Substitute $r = 2$ in and $\pi=3.14$ into the formula: $V=\frac{4}{3}\times3.14\times2^{3}=\frac{4}{3}\times3.14\times8=\frac{4\times3.14\times8}{3}=\frac{100.48}{3}\approx33.5$ in³.

Answer:

B. $33.5$ in³