Question

15. A ball shaped like a sphere has a radius of 2.8 centimeters. Which measurement is closest to the volume of the ball in cubic centimeters? A) 215.2 cm C) 92 cm B) 107.6 cm D) 253.9 cm

Answer 1

Volume of a sphere

We know that the volume of a sphere is given by the following equation:

$Volume=\frac{4}{3}\pi r^3$

where π and r are numbers: π is pi and r is the radius.

Since

π = 3.14

and

r = 2.8 cm, then

$\begin{gathered} Volume=\frac{4}{3}\pi r^3 \\ \downarrow \\ Volume=\frac{4}{3}\cdot3.14\cdot(2.8\operatorname{cm})^3 \end{gathered}$

Since

(2.8 cm)³ = 21.952 cm³,

$\begin{gathered} Volume=\frac{4}{3}\cdot3.14\cdot(2.8\operatorname{cm})^3 \\ \downarrow \\ Volume=\frac{4}{3}\cdot3.14\cdot21.952\operatorname{cm}^3 \\ \downarrow \\ Volume=91.9\operatorname{cm}^3 \end{gathered}$

Since 91.9 is very near to 92, then

91.9 cm³ ≅ 92 cm³

Answer: C. 92 cm³