Question

Adair Advertising has 2 spherical balloons. One has a radius of 3 feet and the other one has a radius of 5 feet. What is the difference in the volume of the two balloons, rounded to the nearest tenth of a cubic foot? Use 3.14 for .
201.1升®
67.0 ft'
205.3 ft3
410.3 £

Answer 1

To find the difference in the volume of the two spherical balloons, we first need to calculate the volume of each balloon using the formula for the volume of a sphere:

\[
V = \frac{4}{3} \pi r^3
\]

where \( V \) is the volume and \( r \) is the radius of the sphere.

**Volume of the first balloon (radius = 3 feet):**

\[
V_1 = \frac{4}{3} \times 3.14 \times (3)^3
\]
\[
V_1 = \frac{4}{3} \times 3.14 \times 27
\]
\[
V_1 = \frac{4}{3} \times 84.78 \approx 113.04 \text{ ft}^3
\]

**Volume of the second balloon (radius = 5 feet):**

\[
V_2 = \frac{4}{3} \times 3.14 \times (5)^3
\]
\[
V_2 = \frac{4}{3} \times 3.14 \times 125
\]
\[
V_2 = \frac{4}{3} \times 392.5 \approx 523.33 \text{ ft}^3
\]

**Difference in volume:**

\[
\text{Difference} = V_2 - V_1
\]
\[
\text{Difference} = 523.33 - 113.04 \approx 410.29 \text{ ft}^3
\]

Rounding to the nearest tenth:

\[
\text{Difference} \approx 410.3 \text{ ft}^3
\]

So, the difference in the volume of the two balloons, rounded to the nearest tenth, is **410.3 ft³**.