Chapter 12.6, Problem 2BCYP

To determine

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

Answer to Problem 2BCYP

280 mm²

Explanation of Solution

Given: The area of the great circle is given as $94$ mm².

Formula used:

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

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

Calculation:

  $\begin{array}{l}\pi r^2=94\\ \Rightarrow r^2=\frac{94}{\pi }\\ \Rightarrow r^2=29.92\end{array}$

Surface area of given hemisphere,

  $\begin{array}{l}=3\pi r^2\\ =3\times \pi \times 29.92\\ =282\\ \sim 280\left(\text{to nearest tenth}\right)\end{array}$

Hence, surface area of given hemisphere is 280 mm².