Chapter 12.6, Problem 2CCYP

To determine

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

Answer to Problem 2CCYP

3050 cm²

Explanation of Solution

Given: The circumference of the great circle is given as $36\pi$ cm.

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:

  $\begin{array}{l}2\pi r=36\pi \\ \Rightarrow r=\frac{36\pi }{2\pi }\\ \Rightarrow r=18\end{array}$

Surface area of given hemisphere,

  $\begin{array}{l}=3\pi r^2\\ =3·\pi ·{\left(18\right)}^2\\ =3\times \pi \times 324\\ =3053.6\\ \sim 3050\left(\text{to nearest tenth}\right)\end{array}$

Hence, surface area of given hemisphere is 3050 cm².