Question

How many more square inches of paint is required to cover a ball whose radius is
60
60 inches than a ball whose radius is
34
34 inches? Use 3.14 for π. Click Here for Help Video



The larger sphere requires
more square inches.

Answer 1

To find out how much more paint is required to cover the larger ball compared to the smaller ball, we need to calculate the surface area of both spheres using the formula for the surface area of a sphere:

\[
S = 4 \pi r^2
\]

where \( S \) is the surface area and \( r \) is the radius. We will use \( \pi \approx 3.14 \).

1. **Calculate the surface area of the larger sphere (radius = 60 inches):**

\[
S_1 = 4 \pi r_1^2 = 4 \cdot 3.14 \cdot (60)^2
\]
\[
= 4 \cdot 3.14 \cdot 3600
\]
\[
= 4 \cdot 3.14 \cdot 3600 = 4 \cdot 11304 = 45216 \text{ square inches}
\]

2. **Calculate the surface area of the smaller sphere (radius = 34 inches):**

\[
S_2 = 4 \pi r_2^2 = 4 \cdot 3.14 \cdot (34)^2
\]
\[
= 4 \cdot 3.14 \cdot 1156
\]
\[
= 4 \cdot 3.14 \cdot 1156 = 4 \cdot 3637.84 = 14551.36 \text{ square inches}
\]

3. **Determine the difference in surface area:**

\[
\text{Difference} = S_1 - S_2
\]
\[
= 45216 - 14551.36
\]
\[
= 30664.64 \text{ square inches}
\]

Thus, the larger sphere requires approximately **30,664.64 square inches** more paint to cover than the smaller sphere.

So we can conclude:

The larger sphere requires **30,664.64** more square inches.