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

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Solution

## 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 cuboidThe volume of a cuboid$\left({V}_{cub}\right)$ is given as${V}_{cub}=l×b×h$where $l,b,h$ are the length, width and height if the cuboid respectively.Substituting the values we get,$⇒$${V}_{cub}=5×4×15c{m}^{3}$$⇒$${V}_{cub}=300c{m}^{3}$Thus the volume of the tin can with rectangular base is $300c{m}^{3}$.Step 2: Calculate the volume of the plastic cylinder with circular base:Given that plastic cylinder is with circular base of diameter $7cm$ and height $10cm$The volume of a cylinder$\left({V}_{cyl}\right)$ is given as ${V}_{cyl}=\frac{{\mathrm{\pi d}}^{2}\mathrm{h}}{4}$where $d,h$ are the diameter and height of the cylinder respectively.Substituting the values we get,$⇒$${V}_{cyl}=\frac{22×{7}^{2}×10}{7×4}c{m}^{3}$$⇒$${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:${V}_{cyl}>{V}_{cub}$ $⇒$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$$⇒$Difference in capacity$=85c{m}^{3}$Hence, the plastic cylinder with circular base has a higher capacity than the tin can with the rectangular base by $85c{m}^{3}$.

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