Question

The base and top radius of a cone is 2.1 m and 0.8 m respectively. The height of the cone is 24 m. What is the volume of frustum of a cone? (use $\pi = 3.14$ ). Insert answer in nearest integer.

Answer 1

Hint:
Here given that base(R) is 2.1 m and top radius(r) is 0.8 m.
Height(h) of the cone is 24 m.
So, we will find the volume of frustum of a cone.
Formula Used: Volume of a frustum of a cone $ = \dfrac{1}{3}\pi h\left( {{R^2} + {r^2} + Rr} \right)$
We have to put the value of R, r, h in the above equation to find the value.

Complete step by step solution:
Here we have given that base(R) is 2.1 m and top radius(r) is 0.8 m.
Height(h) of the cone is 24 m.
So, we have to find the volume of frustum of a cone.
Volume of a frustum of a cone $ = \dfrac{1}{3}\pi h\left( {{R^2} + {r^2} + Rr} \right)$
Now put the value of R, r, h in the above equation
$ = \dfrac{1}{3}\pi \times 24\left( {{{2.1}^2} + {{0.8}^2} + 1.68} \right)$
$ = \dfrac{1}{3}\pi \times 161.52$
$ = \dfrac{1}{3} \times 3.14 \times 161.52$
$ = 169.05{m^3}$
$\therefore $The volume of frustum of a cone up to its nearest integer is $169{m^3}$

Note:
Rounding of a number: Rounding of a number means making a number simpler but keeping its value close to what it was. The result is less accurate, but easier to use.
For example: 1.4869 rounded to tenths is 1.5
Since, as the next digit (8) which is greater than (5).