The cost of painting the total outside surface of a closed cylindrical oil tank at 50 paise per square decimetre
Question:
The cost of painting the total outside surface of a closed cylindrical oil tank at 50 paise per square decimetre is Rs 198. The height of the tank is 6 times the radius of the base of the tank. Find the volume corrected to 2 decimal places
Solution:
Let the radius of the tank be r dm
Then, height = 6r dm
Cost of painting for 50 paisa per $\mathrm{dm}^{2}=$ Rs 198
⟹ 2πr(r + h) = 198
⟹ 2 × 22/7 × r(r + 6r) × 1/2 = 198
⟹ r = 3 dm
Therefore, h = (6 × 3) dm = 18 dm
Volume of the tank $=\pi r^{2} h=22 / 7 \times 9 \times 18=509.14 \mathrm{dm}^{3}$