The radius and height of a right circular cone are in the ratio $5 : 12$ and its volume is $2512$ cubic cm. Find the slant height and radius of the cone. (Use $\pi = 3.14$).

 Given:

The radius and height of a right circular cone are in the ratio $5 : 12$ and its volume is $2512$ cubic cm. 

To do:

We have to find the slant height and radius of the cone.

Solution:

Ratio of the radius and the height of the right circular cone $= 5 : 12$

Volume of the cone $= 2512\ cm^3$

Let the radius of the cone $(r)$ be $5x$ and the height $(h)$ be $12x$.

Therefore,

Volume of the cone $=\frac{1}{3} \pi r^{2} h$

$\frac{1}{3} \times 3.14 \times(5 x)^{2} \times 12 x=2512$

$3.14 \times 25 x^{2} \times 12 x=2512$

$12 \times 25 x^{3}=\frac{2512 \times 3}{3.14}$

$x^{3}=\frac{2512 \times 3}{12 \times 25 \times 3.14}$

$x^{3}=\frac{2512 \times 3 \times 100}{12 \times 25 \times 314}$

$x^{3}=8$

$x^{3}=(2)^{3}$

$\Rightarrow x=2$

Radius of the cone $=5 x$

$=5 \times 2$

$=10 \mathrm{~cm}$

Height of the cone $=12 x$

$=12 \times 2$

$=24 \mathrm{~cm}$

Slant height of the cone $=\sqrt{r^{2}+h^{2}}$

$=\sqrt{(10)^{2}+(24)^{2}}$

$=\sqrt{100+576$

$=\sqrt{676}$

$=26 \mathrm{~cm}$

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Updated on: 10-Oct-2022

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