Question

The base radius of a cylinder is $1\frac{2}{3}$ times its height. The cost of painting its curved surface area at $2paise/c{m}^2$ is Rs. $92.40$. Find the volume of the cylinder.

• A. $80850c{m}^3$
• B. $80580c{m}^3$
• C. $80508c{m}^3$
• D. $800508c{m}^3$

Answer 1

Answer: (A)

$80850c{m}^3$

Let height of cylinder be ${}^{\prime }{h}^{\prime }$ and radius be ${}^{\prime }{r}^{\prime }$ : Then

$r=\frac{5}{3}h$

CSA of cylinder painted $=\frac{92.40}{0.02}=4620{cm}^2$

$\Rightarrow 2\pi rh=4620\Rightarrow 2\times \frac{22}{7}\times \frac{5}{3}\times h=4620\Rightarrow h^2=\frac{4620\times 7\times 3}{2\times 22\times 5}$

$\Rightarrow h^2=441\Rightarrow h=\sqrt{441}=21cm,r=\frac{5}{3}\times 21=35cm$

$\therefore$ Volume = $\pi r^{2}h=\frac{22}{7}\times 35\times 35\times 21=80850{cm}^3$