Question

find the surface area of each figure. round your answers to the nearest tenth, if necessary.
1)
2)
3)
4)
5)
6)

Explanation:

Step1: Recall the formula for the surface area of a sphere

The formula for the surface area of a sphere is \(S = 4\pi r^{2}\), where \(r\) is the radius of the sphere.

Step2: Calculate the surface area for each figure

For figure 1:

Given \(r = 3\) ft.
Substitute \(r = 3\) into the formula:
\(S=4\pi(3)^{2}=4\pi\times9 = 36\pi\approx36\times3.14 = 113.04\approx113.0\) ft².

For figure 2:

Given \(r = 12\) cm.
Substitute \(r = 12\) into the formula:
\(S = 4\pi(12)^{2}=4\pi\times144=576\pi\approx576\times3.14 = 1808.64\approx1808.6\) cm².

For figure 3:

Given \(r = 15.6\) in.
Substitute \(r = 15.6\) into the formula:
\(S=4\pi(15.6)^{2}=4\pi\times243.36 = 973.44\pi\approx973.44\times3.14=3056.6016\approx3056.6\) in².

For figure 4:

Given \(r = 7\) cm.
Substitute \(r = 7\) into the formula:
\(S=4\pi(7)^{2}=4\pi\times49 = 196\pi\approx196\times3.14 = 615.44\approx615.4\) cm².

For figure 5:

Given \(r = 8\) in.
Substitute \(r = 8\) into the formula:
\(S=4\pi(8)^{2}=4\pi\times64 = 256\pi\approx256\times3.14=803.84\approx803.8\) in².

For figure 6:

Given \(r = 10\) mi.
Substitute \(r = 10\) into the formula:
\(S=4\pi(10)^{2}=4\pi\times100 = 400\pi\approx400\times3.14 = 1256.0\) mi².

Answer:

1. \(113.0\) ft²
2. \(1808.6\) cm²
3. \(3056.6\) in²
4. \(615.4\) cm²
5. \(803.8\) in²
6. \(1256.0\) mi²