Q86. - Algebra 2

Question

A circular cell must deliver $18$ watts of energy. If each square centimeter of the cell that is in sunlight produces 0.01 watt of energy, how long must the radius of the cell be?

Step-by-Step Solution

Answer

The radius of the cell must be $23.93\text{ cm}$ longer.

Step 1. Write down the given equation.

It is given that a circular cell delivers 18 watts of energy and each square centimeter of the cell delivers 0.01 watt of energy.

Step 2. Evaluating radius of the cell.

According to question,$1{\text{ cm}}^2$ produces 0.01 watt of energy. Therefore 18 watt of energy delivered by the cell is evaluated as:

$\begin{array}{l}1{\text{ cm}}^2=0.01\text{ watt}\mathrm{....}\left(\text{Given}\right)\\ 1\text{ watt}=100{\text{ cm}}^2\\ 18\text{ watt}=18\times 100{\text{ cm}}^2\\ 18\text{ watt}=1800{\text{ cm}}^2\end{array}$

Now, by formula of area (A) of the circle,

$\begin{array}{l}A=\pi r^2\\ 1800=\frac{22}{7}{r}^2\\ r^2=\frac{1800\times 7}{22}\\ r=\sqrt{\frac{1800\times 7}{22}}\\ r=23.93\text{ cm}\end{array}$

Step 3. Conclusion.

The radius of the cell must be \[23.93\text{ cm}\] longer.