Chapter 12.4, Problem 22WE

To determine

To find: Area of the water surface.

Answer to Problem 22WE

Cans needed to paint the ceiling is 6.

Explanation of Solution

Given information:

A hemispherical bowl with radius 25 contains water whose depth is 10.

Calculation:

And, area of the circle is given by

  $A=\pi r^2$ where $r$ is the radius of the circle.

  

From the above figure, find the radius of the water surface.

Since, triangle ABC is the right angled triangle. Therefore, by Pythagoras theorem

  $\begin{array}{l}{\left(25\right)}^2=A{B}^2+{\left(15\right)}^2\\ 625=A{B}^2+225\\ 625-225=A{B}^2\\ A{B}^2=400\\ AB=20\end{array}$

Therefore,

  $\begin{array}{l}\text{Area of the water surface}=\pi {\left(AB\right)}^2\\ \text{Area of the water surface}=\pi {\left(20\right)}^2\\ \text{Area of the water surface}=400\pi \end{array}$

Hence,

Area of the water surface is $400\pi$ .