# Ex.13.6 Q3 Surface Areas and Volumes Solution - NCERT Maths Class 9

## Question

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

## Text Solution

**Reasoning:**

Volume of the cuboid is *\(lbh\)* and volume of cylinder in\(\begin{align}\,\pi {r^2}h \end{align}\)

**What is known?**

Measurements of cuboid can. Measurements of cylindrical can.

**What is unknown?**

Which can is big and how much** **?

**Steps:**

**Diagram **

Tin Can:

\(\text{Length} \; (l) = 5\ cm \)

\(\text{Breadth}\; (b) = 4\ cm\)

\(\text{Height}\; (h) = 15\ cm\)

\(\text{Capacity = Volume} = l b h\).

\[\begin{align}&= 5 \times 4 \times 15 \\&= 300\,\,c{m^3} \\ \end{align}\]

Plastic Cylinder:

\(\text{Diameter} (2r) =7\; cm\)

Radius\(\begin{align} \,(r) = \frac{7}{2} \end{align}\)cm

\(\text{Height}\; (h) =10\; cm\)

\(\begin{align}\text{Capacity} &= \rm{Volume} = \pi {r^2}h\ \\ &= \frac{{22}}{7} \times \frac{7}{2} \times \frac{7}{2} \times 10\\ &= 385\,\,\,c{m^3} \end{align}\)

Clearly, the plastic cylinder has greater capacity than the tin container.

Difference\(\begin{align} = \,385 - 300 = 85\,c{m^3} \end{align}\)

**Answer:**

The plastic cylindrical can have more capacity than the Tin Can by\(\begin{align}\, = 85\,\,c{m^3} \end{align}\).