Question

The dimensions of a cuboid are $44cm,21cm,12cm$. it is melted and a cone of height $24cm$ is made. Find the radius of its base.

Answer 1

Volume of cuboid$=l\times b\times h$

$=44\times 21\times 12c{m}^3$

Volume of cone$=\frac{1}{3}\pi r^{2}h=\frac{1}{3}\pi r^2\left(24\right)$

Volume of cone $=$ volume of cuboid

$\frac{1}{3}\pi r^2\left(24\right)=44\times 21\times 12c{m}^3$

$\frac{1}{3}\times \frac{22}{7}\times r^2\left(24\right)=44\times 21\times 12c{m}^3$

$r^2=\frac{44\times 21\times 12\times 7\times 3}{22\times 24}$

$r^2=21\times 21$

$r=\sqrt{21\times 21}$

$r=21$

Thus radius of the base is $r=21cm$

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