To paint a cylinder whose radius is half of its height costs ₹237
| To paint a cylinder whose radius is half of its height costs ₹2376. If it costs ₹14 per cm2, Find the height of the cylinder.
A. 8 cm
B. 5 cm
C. 6 cm
D. 3 cm
Please scroll down to see the correct answer and solution guide.
Right Answer is: C
SOLUTION
Given:
Radius × 2 = height
The total cost of painting the whole cylinder = ₹2376
Cost of painting per cm2 = ₹14
Concept used:
Total surface area = Cost of painting whole surface ÷ Cost of painting per unit2
TSA of cylinder = 2πrh + 2πr2 = 2πr × (h + r)
Calculation:
Let radius = x cm and height = 2x cm
TSA = 2πr × (h + r) = Cost of painting whole surface ÷ Cost of painting per unit2
⇒ 2πx × (2x + x) = 2376 ÷ 14
⇒ 6πx2 = 1188/7
⇒ x2 = 9
⇒ x = 3
∴ Radius is 3 cm and Height is 6 cm
