Total surface area of aright circular cylinder is 1848 cm2. The ratio of its total surface area to the curved surface area is 3 : 1. The volume of the cylinder is:(Take $\pi = \frac{22}{7}$)
Answer & explanation
Correct answer: option 3
We know that,
Total surface area of cylinder = 2πr(r + h)
Curved surface area of cylinder = 2πrh
and Volume of cylinder = πr2h
We have, 2πr(r + h) = 1848
\(\frac{ 2πr(r + h)}{ 2πrh }\) = \(\frac{3}{1}\)
= r + h = 3h
= 2h = r
= h = \(\frac{r}{2}\)
Put it in the total surface area formula,
= 2 × \(\frac{22}{7}\) × r × (r + \(\frac{r}{2}\)) = 1848
= 2 × \(\frac{22}{7}\) × r × \(\frac{3r}{2}\) = 1848
= r2 = 7 × 7 × 4
= r = 14
= h = \(\frac{14}{2}\) = 7 cm
= Volume of cylinder = \(\frac{22}{7}\) × 14 × 14 × 7 = 4312 cm3