Question

If height and volume of a cone are 15cm and 500 cm square respectively then find the radius of the base of the cone

Answer 1

Given :

• Height of cone is 15 cm.
• Volume of cone is 500 cm³

To Find :

• Radius of the base of cone.

Solution :

Let the base radius of cone be r cm.

We have the height and volume given.

Use the formula for volume of cone to figure out the base radius.

Formula :

$\large{\boxed{\tt{Volume_{cone}\:=\:\dfrac{1}{3}\:\pi\:r^2\:h}}}$

Block in the data,

$\sf{\longrightarrow{500\:=\:\dfrac{1}{3}\:\pi\:r^2\:15}}$

$\sf{\longrightarrow{500=\dfrac{15\:\pi\:r^2}{3}}}$

$\sf{\longrightarrow{500\:\times\:3\:=\:15\:\pi\:r^2}}$

$\sf{\longrightarrow{1500\:=\:15\:\pi\:r^2}}$

$\sf{\longrightarrow{\dfrac{1500}{15\:\pi}=r^2}}$

$\sf{\longrightarrow{\dfrac{100}{\pi}=r^2}}$

$\sf{\longrightarrow{\dfrac{100}{3.14}=r^2}}$

$\sf{\longrightarrow{31.84=r^2}}$

$\sf{\longrightarrow{\sqrt{31.84}=r^2}}$

$\sf{\longrightarrow{5.64=r}}$

$\large{\boxed{\bold{Radius\:of\:base\:=\:r\:=\:5.64\:cm}}}$

Answer 2

GIVEN:

Height of a cone = 15cm

Volume of the cone = 500cm

TO FIND:

Radius of the base of the cone

SOLUTION:

We know that,

Volume of cone = 1/3 πr²h

500 = 1/3 × 22/7 × r² × 15

500 = 22/7 × r² × 5

500/5 = 22/7 × r²

100 = 22/7 × r²

r² = 100 × 7/22

r² = 700/22

r² = 31.8

r = √31.8

r = 5.64cm

Therefore, radius of base of cone is 5.64cm.