Question

The letter "S" on a billboard is being painted. If the letter is drawn using circles as shown, find the area to be painted. (Radius of the inner circles = 3 ft;
Radius of the outer circles = 5 ft)

• A. $6\pi sq.ft$
• B. $12\pi sq.ft$
• C. $24\pi sq.ft$
• D. $48\pi sq.ft$

Answer 1

The correct option is C $24\pi sq.ft$

$\text{The letter "S" can be divided into two equal}\text{parts as:}$


$\text{Area of each part is}\frac{3}{4}\text{th the difference}\text{between the area of the bigger circle and}\text{the area of the smaller circle.}$

$\text{So, the area of each part is:}$

$\frac{3}{4}\times (\pi \times 5^2-\pi \times 3^2)sq.ft$

$=\frac{3}{4}\times \pi \times 16sq.ft$

$=12\pi sq.ft$

$\text{Hence, the total area of the letter "S" is:}$
$2\times 12\pi =24\pi sq.ft$