The base radius of a cylinder is 5 m more than its height. If the curved surface area of the cylinder is 792 m², then what is the volume of the cylinder (in m³) ? (Use $π =\frac{22}{7}$)

5544

Let us consider that , Height = H 

So, radius = H + 5

Curved surface area of cylinder = 2 × π × radius × height

792 = 2 × \(\frac{22}{7}\) × H × ( 5 + H )

126 = 5H + H²

 H² + 5H - 126 = 0

 H² + 14H - 9H - 126 = 0

H ( H + 14 ) - 9 ( H + 14 ) = 0

( H - 9 ) . ( H + 14 ) = 0

Either ( H - 9 ) = 0 or ( H + 14 ) = 0

( H + 14 ) = 0 is not possible because H can't be negative.

⇒ H = 9

Radius = 9 + 5 = 14

Now ,

Volume = π × r² × H

= \(\frac{22}{7}\) × 196 × 9

= 5544 m³