Question

The volume of the cone whose vertical height is 8 m and the area of the base is $156{m^2}$ is
A. $416{m^3}$
B. $415{m^3}$
C. $312{m^3}$
D. $468{m^3}$

Answer 1

Hint: The volume of the cone is given by where \[h\] is the height of the cone and $r$ is the radius of the cone. We will substitute the given values in the formula of volume of cone to get the required answer.

Complete step-by-step answer:
We have a cone whose height is 8m and the base of the cone is $156{m^2}$
We have to find the volume of the cone.
We know that the volume of the cone is given by \[\dfrac{1}{3}\pi {r^2}h\], where \[h\] is the height of the cone and $r$ is the radius of the cone.

And the base of the cone is a circle, whose area is given by $\pi {r^2}$ where $r$ is the radius of the cone.
On substituting the values of \[h = 8m\] and $\pi {r^2} = 156{m^2}$
Then the volume of the cone is
$\Rightarrow$ $\dfrac{1}{3}\left( {156} \right)\left( 8 \right) = 416{m^3}$
Therefore, the required volume is $416{m^3}$
Hence, option A is correct.

Note: The volume of any object gives the space enclosed by that object. Also the height in the formula of the volume is perpendicular height and not the slant height. The volume of an object is always measured in cubic units.