Chapter 12.6, Problem 17PPS

To determine

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

Answer to Problem 17PPS

530 mm²

Explanation of Solution

Given: The circumference of the great circle is given as $15\pi$ mm.

Formula used:

Surface area of a hemisphere $=3\pi r^2$

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

Calculation:

  $\begin{array}{l}2\pi r=15\pi \\ \Rightarrow r=\frac{15\pi }{2\pi }\\ \Rightarrow r=7.5\end{array}$

Surface area of given hemisphere,

  $\begin{array}{l}=3\pi r^2\\ =3·\pi ·{\left(7.5\right)}^2\\ =3\times \pi \times 56.25\\ =530.1\\ \sim 530\left(\text{to nearest tenth}\right)\end{array}$

Hence, surface area of given hemisphere is 530 mm².