Question

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

(Assume $\pi =\frac{22}{7}$)

Answer 1

Step 1: Calculate the volume of the tin can with rectangular base:

Given that tin can with a rectangular base is of length $5cm$ and width $4cm$, having a height of $15cm$

Since, the can has a rectangular base, the shape of the can will be a cuboid

The volume of a cuboid$\left(V_{cub}\right)$ is given as

$V_{cub}=l\times b\times h$

where $l,b,h$ are the length, width and height if the cuboid respectively.

Substituting the values we get,

$\Rightarrow$$V_{cub}=5\times 4\times 15c{m}^3$

$\Rightarrow$$V_{cub}=300c{m}^3$

Thus the volume of the tin can with rectangular base is $300c{m}^3$.

Step 2: Calculate the volume of the plastic cylinder with circular base:

Given that plastic cylinder is with circular base of diameter $7cm$ and height $10cm$

The volume of a cylinder$\left(V_{cyl}\right)$ is given as $V_{cyl}=\frac{{\mathrm{\pi d}}^2\mathrm{h}}{4}$

where $d,h$ are the diameter and height of the cylinder respectively.

Substituting the values we get,

$\Rightarrow$$V_{cyl}=\frac{22\times 7^2\times 10}{7\times 4}c{m}^3$

$\Rightarrow$$V_{cyl}=385c{m}^3$

Thus the volume of the plastic cylinder with circular base is $385c{m}^3$.

Step 3: Determine the container with greater capacity:

$V_{cyl}>V_{cub}$ $\Rightarrow$The plastic cylinder with circular base has a greater capacity.

The difference in capacity is equal to the difference in volumes.

Difference in capacity$=V_{cyl}-V_{cub}$

$=385-300$

$\Rightarrow$Difference in capacity$=85c{m}^3$

Hence, the plastic cylinder with circular base has a higher capacity than the tin can with the rectangular base by $85c{m}^3$.