Question

A Soft drink is available in two packs-
$\left( i \right)$A tin can with a rectangular base of length 5cm and width 4cm, having a height of 15cm
$\left( {ii} \right)$A plastic cylinder with circular base of diameter 7cm and height 10cm.
Which container has the greater capacity and by how much?

Answer 1

Hint- The volume of tin can\[{\text{ = }}lbh\], we know the volume of cylinder \[{\text{ = }}\pi {r^2}H\]

Given data: -
A tin can with rectangular base i.e. length$\left( l \right) = 5cm$
                                                               Width$\left( b \right) = 4cm$
                                                               Height$\left( h \right) = 15cm$
Therefore volume of tin can \[{\text{ = }}lbh = 5 \times 4 \times 15 = 300c{m^3}\]
Now, given a plastic cylinder with circular base of diameter$ = 7cm$
Therefore radius\[\left( r \right){\text{ = }}\dfrac{{{\text{diameter}}}}{2} = \dfrac{7}{2}cm\]
Height of cylinder$\left( H \right) = 10cm$
$ \Rightarrow $Volume of cylinder \[{\text{ = }}\pi {r^2}H = \dfrac{{22}}{7} \times {\left( {\dfrac{7}{2}} \right)^2} \times 10 = 385c{m^3}\]
Difference of volume \[{\text{ = 385 - 300 = 85c}}{{\text{m}}^3}\]
Hence cylinder has greater capacity by \[{\text{85c}}{{\text{m}}^3}\]
So, this is the required answer.

Note- In such types of questions always remember the formula of volume of tin can with rectangular base and volume of cylinder then calculate the difference of volume, we will get the required answer.