Question

The height of a cone is 3cm if its volume is 300π cm3. Find the diameter of base ​

Answer 1

Volume of cone 1/3x 3x 22/7xr^2=300x22/7
=r^2=300
r=10 sqrt 3
It’s diameter = 20 sqrt 3 cm

Answer 2

Given :

• Height of the cone is 3cm
• Volume of the cone is $\sf 300 \pi cm^3$

To Find :

• diameter of it's base

Solution :

As by the given Condition,

Volume of the cone = $\sf 300 \pi cm^3$

As by Formula,

Volume of the cone is $\dfrac{1}{3}\pi r ^2h$

$\implies \sf 300 \pi cm^3=\dfrac{1}{3}\pi r ^2h$

$\implies \sf 300 {\cancel{\pi }}cm^3=\dfrac{1}{3}\times {\cancel{\pi}} \times r ^2 \times 3$

$\implies \sf 300\: cm^3=\dfrac{1}{{\cancel{3}}}\times r ^2 \times {\cancel{3}}$

$\implies \sf 300\: cm =r ^2$

$\implies \sf r = \sqrt {300} \:cm$

$\implies \sf r = 10\sqrt{3}\: cm$

$\boxed{\sf Diameter = 2 \times Radius }$

$\sf Diameter = 2 \times 10\sqrt{3}$

$\sf Diameter = 20\sqrt{3}$

Required Answer :

Diameter of the given Cone is 20√3 cm