Question

The cost of painting the curved surface area of a cone at $5ps/c{m}^2$ is $Rs35.20$, find the volume of the cone if its slant height is $25cm$.

• A. $1223c{m}^3$
• B. $1979c{m}^3$
• C. $1323c{m}^3$
• D. $1332c{m}^3$

Answer 1

Answer: (B)

$1979c{m}^3$

Curved surface area of cone painted $=\frac{35.20}{0.05}=704{cm}^2$.

$\Rightarrow \pi rl=704{cm}^2\Rightarrow r=\frac{704\times 7}{22\times 25}=8.96cm\approx 9cm$.

Now, $h=\sqrt{l^2-r^2}=\sqrt{{\left(25\right)}^2-{\left(9\right)}^2}=\sqrt{625-81}=\sqrt{544}=23.32cm$.

Therefore, Volume of cone $=\frac{1}{3}\pi r^{2}h=\frac{1}{3}\times \frac{22}{7}\times 9\times 9\times 23.32=1979{cm}^3$.

Hence, option $B$ is correct.