Question

It costs Rs.$2200$ to paint the inner curved surface of a cylindrical vessel $10m$ deep. If the cost of painting is at the rate of Rs.$20$ per $m^2$. Find capacity of the vessel.

• A. $96.25$ $m^3$
• B. $56.25$ $m^3$
• C. $96.75$ $m^3$
• D. $91.25$ $m^3$

Answer 1

Answer: (A)

If the cost of painting is at the rate of Rs.$20$ per $m^2$, then it costs Rs. $2200$ for the area $\frac{2200}{20}=110m^2$
Hence, the inner curved surface area of the vessel is $110m^2$

Curved Surface Area of a Cylinder $=2\pi Rh$
Hence, CSA of the given cylinder $=2\times \frac{22}{7}\times r\times 10=110$

$=>r=1.75m$

Radius of the base of the cylinder is $1.75m$

Volume of a Cylinder $=\pi R^{2}h$
Hence, capacity of the given vessel $=\frac{22}{7}\times 1.75\times 1.75\times 10=96.25m^3$