Question

The volume of right circular cone of height 8 cm and radius of the base is 3 cm is ………………..

Answer 1

Hint: To solve the question, we have to substitute the given value of height and base radius of the right circular cone in the formula of the volume of the cone.

Complete step-by-step answer:
Given that the height of the right circular cone and the radius of the base of the right circular cone is equal to 8 cm and 3 cm respectively. Using these parameters we can draw the 3D projection of the cone to visualise the volume of the cone, which helps in better understanding.

We know that the formula of the volume of cone is equal to \[\dfrac{\pi {{r}^{2}}h}{3}\] cubic units.
Where \[h,r\] are the height and the base radius of the right circular cone.
By substituting the given values in the above formula, we get
The volume of the given right circular cone \[=\dfrac{\pi {{(3)}^{2}}(8)}{3}\]
\[=\pi \times 3\times 8\]
\[=24\pi \]cubic cm.
We know that the value of \[\pi =3.14\]
Substitute the value of \[\pi \] to calculate the volume of the given right circular cone.
\[\therefore \] The volume of the given right circular cone \[=24\times 3.14\] \[=75.36\] cubic cm.

Note: The possibility of mistake can be the confusion caused due to the mentioning of the right circular cone in the question. A right circular cone is a normal cone with a property that the slant height, base radius, height of the cone form sides of the right-angled triangle with slant height as hypotenuse. This property will help to calculate the slant height value. The alternative idea to reach the solution is to calculate the volume of cylinder \[=\pi {{r}^{2}}h\] and the one third of this value will provide the volume of the cone. The general caution for this model of questions is to keep all the given measurements in one system of units, either in meters or centimetres.