Question

A bus stop is barricaded from the remaining part of the road, by using 50 hollow cones made of recycled cardboard. Each cone has a base diameter of 40 cm and height 1 m. If the outer side of each of the cones is to be painted and the cost of painting is Rs 12 per m2, what will be the cost of painting all these cones? (Use $\pi$ = 3.14 and take 1.04 = 1.02)

Answer 1

Slant height, l = $\sqrt{(r² + h²)}$ where h is the height of the cone.
Diameter, d = 40cm = $\frac{40}{100}$ m = 0.4m
Radius, r = $\frac{0.4}{2}$ m = 0.2 m
Height, h = 1 m
Slant height, $l = \sqrt{(0.2)² + (1)²}$
$= \sqrt{0.04m² + 1m²}$
$= \sqrt{1.04} = 1.02$ m (given)

The curved surface area = $\pi rl$
= 3.14 × 0.2m × 1.02m
= 0.64056 m2

Curved surface area of 50 cones = 50 × 0.64056 m2 = 32.028 m2
Cost of painting 1 m2 area = Rs 12
Cost of painting 32.028 m2 area = Rs (32.028 × 12)
= Rs 384.336
= Rs 384.34 (approximately)
Therefore, it will cost Rs 384.34 in painting 50 such hollow cones.