The curved surface area of a right circular is 616 cm² and area of its base 38.5 cm². What is the volume (in cm³) of the cylinder ? (Take $ \pi =\frac{22}{7}$)

1078

We know that,

The area of the base of a right circular cylinder = π × (radius)²

The curved surface area of a right circular cylinder = 2 × π × (radius) × (height)

The volume of a right circular cylinder = π × (radius)² × (height)

We have,

The curved surface area of a right circular cylinder = 616 cm²

The area of the base of the right circular cylinder = 38.5 cm²

πR² = 38.5

= \(\frac{22}{7}\) × R² = \(\frac{77}{2}\)

= R² = \(\frac{77}{2}\) × \(\frac{7}{22}\)= \(\frac{49}{4}\)

= R = \(\frac{7}{2}\)

Also, 2 × \(\frac{22}{7}\) × \(\frac{7}{2}\) × (Height) = 616

Height = 616 × \(\frac{1}{2}\) \(\frac{7}{22}\) × \(\frac{2}{7}\) = 28 cm

Then, the volume = \(\frac{22}{7}\) × \(\frac{49}{4}\) × 28 = 1078 cm³