Question

A rectangular sheet of acrylic is 34 cm by 24 cm. From it, 64 circular buttons, each of diameter 3.5 cm, have been cut out. Find the area of the remaining sheet.

Answer 1

Area of the acrylic sheet = 34 cm × 24 cm = 816 cm²
Given that the diameter of a circular button is 3.5 cm.
∴ Radius of the circular button (r)= $\left(\frac{3.5}{2}\right)$ cm = 1.75 cm
∴ Area of 1 circular button = ${\mathrm{\pi r}}^2$
= $\left(\frac{22}{7}\times 1.75\times 1.75\right)$ cm²
= 9.625 cm²
∴ Area of 64 such buttons = (64 × 9.625) cm² = 616 cm²
Area of the remaining acrylic sheet = (Area of the acrylic sheet - Area of 64 circular buttons)
= (816 - 616) cm² = 200 cm²