Question

A solid metallic cylinder is cut into two identical halves along its height (as shown in the diagram). The diameter of the cylinder is 7 cm and the height is 10 cm.

Find:

1. The total surface area (both the halves).
2. The total cost of painting the two halves at the rate of ₹ 30 per cm² `("Use"  π = 22/7)`.
   

Answer 1

(a) Diameter of cylinder (d) = 7 cm

Radius of cylinder (r) = `d/2 = 7/2 = 3.5 cm`

Height of cylinder (h) = 10 cm

Total surface area (both the halves) = Total surface area of cylinder + Area of two rectangles

= [2πr(h + r)] + [2 × (l × b)]

= [2πr(h + r)] + [2 × (h × d)]

`= [2xx 22/7xx3.5xx(3.5+10)] + 2xx10xx7`

= (2 × 22 × 0.5 × 13.5) + 140

= 297 + 140

= 437 cm².

Hence, total surface area of both the halves = 437 cm².

(b) Total cost of painting the two halves = Total surface area × Rate

= 437 × 30

= ₹ 13,110