Question

A round balloon has a diameter of 7 inches
Which of the following is closest to the number of
cubic inches of air can it hold?
A) 181 in
B) 189 in
C) 196 in
D) 208 in
E) 210 in
None of the above
+3

Answer 1

Answer:

The right answer is approximately 210.031 cubic inches. (Answer: E)

Step-by-step explanation:

First, we need to convert the diameter ($D$), in inches, of the round balloon to an entirely decimal mode:

$D = 7\,in + \frac{3}{8}\,in$

$D = \frac{56 + 3}{8}\,in$

$D = \frac{59}{8}\,in$

$D \approx 7.375\,in$

The volume of the balloon is modelled after the volume function of a sphere ($V$), in cubic inches:

$V = \frac{\pi}{6}\cdot D^{3}$ (1)

If we know that $D \approx 7.375\,in$, then the volume of the round balloon is:

$V = \frac{\pi}{6}\cdot D^{3}$

$V = \frac{\pi}{6} \cdot (7.375\,in)^{3}$

$V \approx 210.031\,in^{3}$

Hence, the right answer is approximately 210.031 cubic inches.