Question

The radii of two circular ends of frustum shape bucket are 14cm and 7cm. Height of the bucket is 30cm. How many litres of water it can hold? (1 litre=1000cm)?

Answer 1

Hint: We are given the radius and height of the bucket. We will substitute the values in the formula of the volume of the frustum, which is $V = \dfrac{{\pi h}}{3}\left( {{R^2} + Rr + {r^2}} \right)$, where, $r$ and $R$ are the radii of the frustum and $h$ is the height of the frustum.

Complete step-by-step answer:
We are given the radii of two ends of bucket of the shape frustum
We have to find the litres of water it can hold, that is we will find the volume of frustum.
As it is known that the volume of the frustum is given as $V = \dfrac{{\pi h}}{3}\left( {{R^2} + Rr + {r^2}} \right)$

Substitute 14 for $R$, 7 for $r$ and 30 for $h$ in the above equation.
$
  V = \dfrac{{\pi \left( {30} \right)}}{3}\left( {{{\left( {14} \right)}^2} + \left( {14} \right)\left( 7 \right) + {{\left( 7 \right)}^2}} \right) \\
   \Rightarrow V = 3430\pi \\
$
Now, substitute $\pi = \dfrac{{22}}{7}$
$V = 3430\left( {\dfrac{{22}}{7}} \right) = 10780c{m^3}$
But, we have to find the volume of the frustum in litres.
We know that $1litre = 1000c{m^3}$
Hence, divide the calculated volume by 1000 to find the volume of the bucket in litres.
$
  V = \dfrac{{10780}}{{1000}}{\text{litres}} \\
   \Rightarrow V = 10.78{\text{litres}} \\
$
Hence, the amount of water a bucket can hold is 10.78 litres.

Note: Volume of any object gives the amount of space enclosed by that object. Volume is always measured in cubic units. Students must know the formula of the volume of the frustum and substitute the values correctly in order to get the correct answer.