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.