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?

Short answer

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

Step-by-step solution

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.