Question

A cone is 8.4 cm high and the radius of its base is 2.1cm. It is melted and recast into 10 smaller cones of radius 1.4cm. Find the height of the smaller cones formed.

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Answer 1

Let the height of the smaller cone be h cm.
$\frac{1}{3}\pi R^{2}H=\frac{1}{3}\pi r^{2}h\times 10$

$\frac{1}{3}\times \frac{22}{7}\times (2.1{)}^2\times 8.4=\frac{1}{3}$ $\times \frac{22}{7}\times (1.4{)}^2\times h\times 10$

$h=\frac{2.1\times 2.1\times 8.4}{1.4\times 1.4\times 10}$
$h=1.89cm$