Question

The radius and slant height of a cone is \[10cm\] and \[26cm\], find its volume.

Answer 1

Hint: In the given question, we have been given a problem involving the use of a right circular cone. We have been given the radius and the slant height of the cone. We have to find the volume of the cone. To do that, we are first going to find the vertical height of the cone. Then we are going to write the formula of volume. Then we are going to substitute the values and find the answer.

Formula used:
We are going to use the formula of volume of a cone, which is:
\[V = \dfrac{1}{3}\pi {r^2}h\]

Complete step by step solution:

Given, radius, \[r = 10cm\]
Slant height, \[l = 26cm\]
First, we are going to find the value of vertical height,
\[h = \sqrt {{l^2} - {r^2}} = \sqrt {{{26}^2} - {{10}^2}} = \sqrt {676 - 100} = \sqrt {576} = 24cm\]
Now, we are going to use the formula of volume of a cone, which is:
\[V = \dfrac{1}{3}\pi {r^2}h\]
Putting in the values into the formula,
\[V = \dfrac{1}{3} \times \dfrac{{22}}{7} \times {10^2} \times 24 = \dfrac{{17600}}{7} = 2514\dfrac{2}{7} \approx 2514.28c{m^3}\]
Hence, the volume of the cone is approximately \[2514.28c{m^3}\].

Note: In the given question, we had to find the volume of a cone. We were given the radius and the slant height of the cone. We calculated it by first finding the vertical height of the cone, then applying the formula of volume putting in the values, simplifying the expression and finding the answer. So, it is very important that we know all the formulae and the results of the formulae.