Question

The cost of painting the total surface area of cone at 25 paise per ${cm}^2$ is Rs 176. Find the volume of the cone, if its slant height is 25cm.

Answer 1

Total surface area of cone $=\pi rl+\pi r^2$

where $l$ is the slant height & $r$ is radius

TSA of cone $=\frac{totalcost}{cost/c{m}^2}=\frac{176}{0.25}=704c{m}^2$

So $\pi rl+\pi r^2=704$

$\Rightarrow \pi r[l+r]=704$

$\Rightarrow \frac{22}{7}r[25+r]=704$

$\Rightarrow r^2+25r-224=0$

$\Rightarrow (r+32)(r-7)=0$

$\Rightarrow r=7,-32$ [radius cannot be negative]

$\Rightarrow r=7$

volume of cone $=\frac{1}{3}\pi r^2\sqrt{l^2-r^2}$

$=\frac{1}{3}\times \frac{22}{7}\times 7\times 7\times \sqrt{{25}^2-7^2}$

$=1231.504$