Question

The radius of the end of the bucket of height 24 cm is 15 cm and 5 cm. Find its capacity? (Take\[\pi {\text{ }} = \dfrac{{22}}{7}\])

Answer 1

Hint: The given container is of frustum shape and volume of frustum is \[\dfrac{1}{3}\pi h\left[ {{{\left( {{r_1}} \right)}^2} + {r_1}{r_2} + {{\left( {{r_2}} \right)}^2}} \right]\]and so classify various values from the question and put that into the formula of frustum and hence we can calculate the capacity of container.

Complete step-by-step answer:
Put the value of radii and height in the formula of volume of frustum as the formula given below :
$ \Rightarrow $\[V = \dfrac{1}{3}\pi h\left[ {{{\left( {{r_1}} \right)}^2} + {r_1}{r_2} + {{\left( {{r_2}} \right)}^2}} \right]\]
Now put the value of height and radii of the container given.
$ \Rightarrow $\[V = \dfrac{1}{3}\pi 24\left[ {{{\left( {15} \right)}^2} + 15 \times 5 + {{\left( 5 \right)}^2}} \right]\]
$ \Rightarrow $\[V = \dfrac{1}{3}\pi \left( {24} \right)\left( {325} \right)\]
Calculate the value as stated above
$ \Rightarrow $\[V = \pi \left( 8 \right)\left( {325} \right)\]
$ \Rightarrow $\[V = 8171.43c{m^3}\]
Hence the capacity of the container is \[8171.43c{m^3}\]

Note: Remember the formula of volume of frustum and classify the height and both the radii carefully and calculate the value of the volume properly and also use the given value of $\pi $as per mentioned in the question. In order to deem down confusion, draw the diagram of frustum and represent each and every quantity properly . Frustum is like the structure of a half cut cone.
A conical frustum is a frustum created by slicing the top off a cone (with the cut made parallel to the base).