Question : The amount of concrete required to build a concrete cylindrical pillar whose base has a perimeter of 8.8 m and a curved surface area of 17.6 m2 is:
(Take $\pi =\frac{22}{7}$)
Option 1: $8.325\;\mathrm{m^3}$
Option 2: $9.725\;\mathrm{m^3}$
Option 3: $10.5\;\mathrm{m^3}$
Option 4: $12.32\;\mathrm{m^3}$
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Correct Answer: $12.32\;\mathrm{m^3}$
Solution :
We have a perimeter of $8.8\;\mathrm{m}$ and a curved surface area of $17.6\;\mathrm{m^2}$ of a cylindrical pillar.
Let $r$ be the radius and $h$ be the height of the cylinder.
The perimeter of the base of the cylindrical pillar $=8.8\;\mathrm{m}$
⇒ $2\pi r = 8.8$
$\therefore r = \frac{8.8}{2\pi}=1.4\;\mathrm{m}$
The curved surface area of a cylindrical pillar $=17.6\;\mathrm{m^2}$
⇒ $2\pi rh = 17.6$
$\therefore h = \frac{17.6}{2\pi r}= \frac{17.6}{2\pi ×1.4}=2\;\mathrm{m}$
The volume of a cylindrical pillar $=\pi r^2h= \pi \times (1.4)^2 \times 2=12.32\;\mathrm{m^3}$
Hence, the correct answer is $12.32\;\mathrm{m^3}$.
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