Explanation:
The lateral surface area of a cone is A = π r L, where L = √(r² + h²) is the slant height.
The lateral surface area of a cylinder is A = 2 π r H.
The area of the cylinder's base is A = π r².
The total area is therefore:
A = π r L + 2 π r H + π r²
A = π r² + (π L + 2 π H) r
The total cost of painting the surface is Rs. 1531.20 at a rate of Rs. 140 per 100 cm². Therefore the total surface area is:
A = Rs. 1531.20 / (Rs. 140 / 100 cm²)
A = 1093.71 cm²
Plug in and solve for r:
1093.71 = π r² + (10π + 42π) r
348.14 = r² + 52r
r² + 52r − 348.14 = 0
r = [ -52 ± √(52² − 4(1)(-348.14)) ] / 2
r = [ -52 ± √(52² − 4(1)(-348.14)) ] / 2
r = (-52 ± 64) / 2
r = -58 or 6
Since r > 0, r = 6.
Solve for h:
L² = r² + h²
10² = 6² + h²
h = 8 cm