Question

a sphere has a radius of 3.5 cm. calculate its volume using π ≈ 3.14.
a. 179.50 cm³
b. 181.45 cm³
c. 178.58 cm³
d. 179.67 cm³

if the volume of a sphere is 36π cm³, what is its radius?
a. 4 cm
b. 2 cm
c. 1 cm
d. 3 cm

Explanation:

Step1: Volume formula of sphere

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

Step2: Calculate the volume for the first question

Given $r = 3.5$ cm and $\pi\approx3.14$.
Substitute into the formula:
$V=\frac{4}{3}\times3.14\times(3.5)^{3}$
$=\frac{4}{3}\times3.14\times42.875$
$=\frac{4\times3.14\times42.875}{3}$
$=\frac{538.51}{3}\approx179.50$ cm³.

Step3: Solve for the radius in the second question

Given $V = 36\pi$ cm³.
Using the formula $V=\frac{4}{3}\pi r^{3}$, we have $36\pi=\frac{4}{3}\pi r^{3}$.
Cancel out $\pi$ on both sides: $36=\frac{4}{3}r^{3}$.
Then $r^{3}=36\times\frac{3}{4}=27$.
Take the cube - root of both sides: $r = 3$ cm.

Answer:

1. A. $179.50$ cm³
2. D. $3$ cm