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If the height of a cylinder is 4 times its circumference, the volume of the cylinder in terms of its circumference, $$c$$ is
Answer & Solution
Correct Answer:
Option
B
Here h = 4c,
Volume of cylinder = πr2h
$$ = \frac{{4\pi \times \pi {r^2}h}}{{4\pi }}$$
(Multiply 4π both in Numerator & Denominator)
$$\eqalign{ & = \frac{{{{\left( {2\pi r} \right)}^2} \times \left( {4c} \right)}}{{4\pi }} \cr & = \frac{{{c^3}}}{\pi } \cr} $$
Volume of cylinder = πr2h
$$ = \frac{{4\pi \times \pi {r^2}h}}{{4\pi }}$$
(Multiply 4π both in Numerator & Denominator)
$$\eqalign{ & = \frac{{{{\left( {2\pi r} \right)}^2} \times \left( {4c} \right)}}{{4\pi }} \cr & = \frac{{{c^3}}}{\pi } \cr} $$
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