Question

For a cone \[r = 1.4cm\] and \[h = 6cm\] . Find the volume of the cone. \[\left( {\pi = \dfrac{{22}}{7}} \right)\]

Answer 1

Hint:In order to solve the given problem first we will draw the cone for better understanding of different terms and mentioned dimensions of the cone. Further by using the general formula for the volume of the cone, we will find the result of the problem also we will use the given value of pi in the question rather than using the decimal approximate value.

Complete step-by-step answer:
We will solve the problem by understanding the concept with the help of a given figure.

Given that:
Radius of the cone is \[r = 1.4cm\]
Height of the cone is \[h = 6cm\]
As we know that for the general cone with radius x and height y the volume of the cone is given as:
\[V = \dfrac{1}{3}\pi {r^2}y\]
Using the above formula for the given cone we have the volume of the cone is given as:
\[V = \dfrac{1}{3}\pi {r^2}h\]
Let us substitute the values in the formula:
\[
   \Rightarrow V = \dfrac{1}{3} \times \pi \times {\left( {1.4} \right)^2} \times 6 \\
   \Rightarrow V = \dfrac{1}{3} \times \dfrac{{22}}{7} \times 1.4 \times 1.4 \times 6 \\
 \]
Let us further simplify the term to get the final volume of the given cone.
\[
   \Rightarrow V = 22 \times 0.2 \times 1.4 \times 2 \\
   \Rightarrow V = 12.32c{m^2} \\
 \]
Hence, the volume of the cone is \[12.32c{m^2}\]

Note:In order to solve such problems students must remember the general formula for the volume, curved surface area, total surface area and other terms for some general geometric shapes and figures like cone, cylinder, cube etc. Students must remember to use the value of constant same as that mentioned in the problem. But when not mentioned students may take the convenient value as remembered.