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Volume and Surface Area — MATHS STD 9 — Question

Rajasthan BoardEnglish MediumSTD 9MATHSVolume and Surface Area5 Marks
Question
A soft drink is available in two packs:
  1. A tin can with a rectangular base of length $5\ cm,$ breadth $4\ cm$ and height $15\ cm.$
  2. A plastic cylinder with circular base of diameter $7\ cm$ and height $10\ cm.$
Which container has greater capacity and by how much?
✓

Answer

  1. For a tin of rectangular base,
Length $= 5\ cm$
Breadth $= 4\ cm$
Height $= 15\ cm$
$\therefore$ Volume of a tin can $=$ Length $\times$ Breadth $\times$ Height
$= (5 \times 4 \times 15)cm^3$
$= 300\ cm^3$
  1. For a cylinder with circular base,
Diameter $= 7$
$\Rightarrow$ Radius $=\text{r}=\frac{7}{2}\text{ cm}$
Height$ = h = 10\ cm$
$\therefore$ Volume of cylinder $=\pi\text{r}^2\text{h}$
$=\Big(\frac{22}{7}\times\frac{7}{2}\times\frac{7}{2}\times10\Big)\text{ cm}^3$
$=385\text{ cm}^3$
$\Rightarrow$ Volume of plastic cylinder is greater than volume of a tin can.
Difference in volume $= (385 - 300) = 85\ cm^3$
Thus, a plastic cylinder has more capacity that a tin can by $85\ cm^3.$

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