Question

4 focus lights are to be fixed on a square aluminum plate with side length, l = 28 inch. Circles are cut in the plate to accommodate the lights. After the required alterations the aluminum plate looks similar to the figure shown. What would be the area of the aluminum plate after alterations?

• A. 168 sq inches
• B. 180 sq inches
• C. 200 sq inches
• D. 169 sq inches

Answer 1

The correct option is A

168 sq inches

The area of the aluminum sheet = Area of the square – Area of the cut-out circles

The area of the square = $l^2$

= ${28}^2$

= 784 sq inches

From the figure it is clear that the length of the square is equal to the sum of the diameters of the 2 circles.

Let us assume, the radius of the circle is ‘r’.

Then, 2d = l

4r = l

r = $\frac{28}{4}$

= 7 inch

The area of 1 circle =$\pi \times r^2$

=$\left(\frac{22}{7}\right)\times 7^2$

= 154 sq inches

The total area of the circles is = 4 $\times$ area of 1 circle

= 4 $\times$ 154

= 616 sq inches

The area of the aluminum plate is = area of the square – area of the circles

= 784 – 616

= 168 sq inches

The area of the aluminum after alteration is 168 sq inches.