Question

if the height of a cone is equal to diameter of its base, find the volume of the cone​

Answer 1

Step-by-step explanation:

cone is:

\text{Volume of cone } = \frac{2}{3} \pi r^3Volume of cone =

3

2

πr

3

Solution:

The volume of cone is given as:

\text{Volume of cone } = \frac{1}{3} \times \pi r^2 hVolume of cone =

3

1

×πr

2

h

Where,

"r" is the radius

"h" is the height

Given that,

height of a cone is equal to diameter of its base

Therefore,

\begin{gathered}h = d\\\\We\ know\ that\ diameter = 2\ radius\end{gathered}

h=d

We know that diameter=2 radius

Thus,

h = 2r

Therefore, substitute h = 2r in formula,

\begin{gathered}\text{Volume of cone } = \frac{1}{3} \times \pi r^2 (2r)\\\\\text{Volume of cone } = \frac{2}{3} \pi r^3\end{gathered}

Volume of cone =

3

1

×πr

2

(2r)

Volume of cone =

3

2

πr

3

Thus the volume of cone is found