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 determine how many more square inches of paint is required to cover a ball with a radius of 62 inches compared to a ball with a radius of 14 inches, we need to calculate the surface area of both spheres using the formula for the surface area of a sphere:

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

where \( A \) is the surface area and \( r \) is the radius of the sphere.

**Step 1: Calculate the surface area of the larger sphere (radius = 62 inches)**

\[
A_{62} = 4 \times 3.14 \times (62^2)
\]

First, calculate \( 62^2 \):

\[
62^2 = 3844
\]

Now plug this value into the surface area formula:

\[
A_{62} = 4 \times 3.14 \times 3844
\]
\[
A_{62} = 4 \times 3.14 \times 3844 = 4 \times 12058.16 = 48232.64 \text{ square inches}
\]

**Step 2: Calculate the surface area of the smaller sphere (radius = 14 inches)**

\[
A_{14} = 4 \times 3.14 \times (14^2)
\]

First, calculate \( 14^2 \):

\[
14^2 = 196
\]

Now plug this value into the surface area formula:

\[
A_{14} = 4 \times 3.14 \times 196
\]
\[
A_{14} = 4 \times 615.44 = 2461.76 \text{ square inches}
\]

**Step 3: Calculate the difference in surface area**

Now we subtract the surface area of the smaller sphere from the surface area of the larger sphere:

\[
\text{Difference} = A_{62} - A_{14}
\]
\[
\text{Difference} = 48232.64 - 2461.76
\]
\[
\text{Difference} = 45770.88 \text{ square inches}
\]

Therefore, the larger sphere requires **45770.88** more square inches of paint.