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}$)
Answer & explanation
Correct answer: option 4
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