Question

The W.M. Keck Observatory, located on top of the dormant volcano Mauna Kea in Hawaii, has two telescopes. Each telescope has a mirror composed of 36 identical sections that are fitted together. The total area of the mirror is about 75.8 square meters. Find the area of each section of the mirror to the nearest tenth of a square meter.

Short answer

Area of section of the mirror $=2.1$square meter.

Step-by-step solution

Step-1- Writing formula from given information

Let $x$be the area of each section of mirror.

Total area = Number of mirrors $\times$ Area of each section of mirror.

Step-2-Solve for value of x

On substituting values, we get

$75.8=36x$.

Dividing with $36$on both sides We get

$\begin{array}{l}\frac{75.8}{36}=\frac{36x}{36}\\ x=\frac{75.8}{36}\\ x=2.105\end{array}$

Step-3-Conclusion

As we are asked to round off to nearest tenth, we get

$x=2.1$.

Therefore, the area of section of the mirror $=2.1$square meter.