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 $π =\frac{22}{7}$)
Answer & explanation
Correct answer: option 3
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