Chapter 12.6, Problem 4CYU

To determine

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

Answer to Problem 4CYU

160 cm²

Explanation of Solution

Given: The circumference of the great circle is given as $26$ 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:

  $\begin{array}{l}2\pi r=26\\ \Rightarrow r=\frac{26}{2\pi }\\ \Rightarrow r=4.1\end{array}$

Surface area of given hemisphere,

  $\begin{array}{l}=3\pi r^2\\ =3·\pi ·{\left(4.1\right)}^2\\ =3\times \pi \times 17.1\\ =161.4\\ \sim 160\left(\text{to nearest tenth}\right)\end{array}$

Hence, surface area of given hemisphere is 160 cm².