Question

4 focus lights are to be fixed on a square aluminium plate of side 28 inches. Circles are cut in the plate to accommodate the lights. After the required alterations, the aluminium plate looks similar to the figure shown below. What is the area of the aluminium portion after alterations?

• A. 168 sq inches
• B. 160 sq inches
• C. 148 sq inches
• D. 120 sq inches

Answer 1

The correct option is A

168 sq inches

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

The area of the square = $l^2$

= ${28}^2$

= 784 sq inches

From the figure, it is clear that the side of the square is equal to the sum of the diameter of the 2 circles.

Let us assume, the radius of the circle as ‘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 aluminium portion = area of the square – area of the circles

= 784 – 616

= 168 sq inches

The area of the aluminium portion after the alteration is 168 sq inches.