Question

The volume of a cone is $9856cucm$. If the diameter of its base is $28cm$, what is its height and its slant height?

Answer 1

Volume of a cone$=9856$cu.cm(given)

Diameter of the base$=28$cm(given)

$\Rightarrow$ Radius of the base$=\frac{28}{2}=14$cm

Volume of a cone$=\pi r^{2}h$

$\Rightarrow 9856=\frac{22}{7}{14}^2\times h$

$\Rightarrow 9856=\frac{22}{7}\times 14\times 14h$

$\Rightarrow$ Slant height$=\frac{9856\times 7}{22\times 14\times 14}$

$\Rightarrow l=\frac{352}{22}=16$cms on simplification

We have $h=\sqrt{l^2+r^2}=\sqrt{{16}^2+{14}^2}=\sqrt{256+196}=\sqrt{452}=21.26$cms