Chapter 12.6, Problem 2ACYP

To determine

To find the surface area of given sphere to the nearest tenth.

Answer to Problem 2ACYP

820 ft²

Explanation of Solution

Given: The circumference of the great circle is given as $16.2\pi$ ft.

Formula used:

Surface area of a sphere $=4\pi r^2$

And circumference of great circle of a sphere $=2\pi r$ , where r is the radius of the sphere.

Calculation:

  $\begin{array}{l}2\pi r=16.2\pi \\ \Rightarrow r=\frac{16.2\pi }{2\pi }\\ \Rightarrow r=8.1\end{array}$

Surface area of given sphere,

  $\begin{array}{l}=4\pi r^2\\ =4·\pi ·{\left(8.1\right)}^2\\ =4\times \pi \times 65.61\\ =824.4\\ \sim 820\left(\text{to nearest tenth}\right)\end{array}$

Hence, surface area of given sphere is 820 ft².