Question

The curved surface area of a cone is $1159\frac{5}{7}c{m}^2$.Area of its base is $254\frac{4}{7}c{m}^2$.Find its volume.

Answer 1

Given curved surface area of the cone is $1159\frac{5}{7}c{m}^2$ and the area of its base is $254\frac{4}{7}{m}^2$

Then area of base =$\pi r^2=254\frac{4}{7}=\frac{1782}{7}$

$\Rightarrow \frac{22}{7}{r}^2=\frac{1782}{7}$

$\Rightarrow r^2=\frac{1782}{22}=81$$\Rightarrow r=9$ cm

The curved surface area $=\pi rl=1159\frac{5}{7}$

$\Rightarrow \frac{22}{7}\times 9\times l=\frac{8118}{7}$

$\Rightarrow l=\frac{8118}{22\times 9}=41$ cm

Then height of cone =$\sqrt{(41{)}^2-(9{)}^2}=\sqrt{1681-81}=\sqrt{1600}=40$ cm

So, volume of cone =$\frac{1}{3}\pi r^{2}h=\frac{1}{3}\times \frac{22}{7}\times (9{)}^2\times 40$

$=\frac{22\times 81\times 40}{3\times 7}=\frac{71280}{21}=3394\frac{2}{4}c{m}^3$