Question

How many more square inches of paint is required to cover a ball whose radius is 62 inches than a ball whose radius is 14 inches?
Use 3.14 for π. Click Here for Help Video



The larger sphere requires___ more square inches.

Answer 1

To find how much more paint is required to cover the larger ball compared to the smaller ball, we need to calculate the surface areas of both spheres and then find the difference.

The formula for the surface area \( A \) of a sphere is given by:

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

where \( r \) is the radius of the sphere.

1. Calculate the surface area of the larger ball (radius = 62 inches):

\[
A_1 = 4 \times 3.14 \times (62)^2
\]

First, we compute \( 62^2 \):

\[
62^2 = 3844
\]

Now plug this value into the surface area formula:

\[
A_1 = 4 \times 3.14 \times 3844
\]

Calculating \( 4 \times 3.14 \):

\[
4 \times 3.14 = 12.56
\]

Now calculate:

\[
A_1 = 12.56 \times 3844 \approx 48303.04 \text{ square inches}
\]

2. Calculate the surface area of the smaller ball (radius = 14 inches):

\[
A_2 = 4 \times 3.14 \times (14)^2
\]

First, we compute \( 14^2 \):

\[
14^2 = 196
\]

Now plug this value into the surface area formula:

\[
A_2 = 4 \times 3.14 \times 196
\]

Calculating \( 4 \times 3.14 \):

\[
A_2 = 12.56 \times 196
\]

Now calculate:

\[
A_2 \approx 2469.76 \text{ square inches}
\]

3. Now, find the difference in surface areas:

\[
\text{Difference} = A_1 - A_2 \approx 48303.04 - 2469.76 \approx 45833.28 \text{ square inches}
\]

Thus, the larger sphere requires approximately **45833.28** more square inches of paint than the smaller sphere.

The answer is:

The larger sphere requires **45833.28** more square inches.