Question

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

• A. $h=1.89cm$
• B. $h=1.54cm$
• C. $h=1.72cm$
• D. $h=1.79cm$

Answer 1

The correct option is A $h=1.89cm$

We know that,
Volume of a cone
$=\frac{1}{3}\pi R^{2}H$

Let the height of the smaller cone be $hcm$.

Now,
Volume of initial cone
= Volume of all smaller cones formed

$\Rightarrow \frac{1}{3}\pi R^{2}H=\frac{1}{3}\pi r^{2}h\times 10$

$\Rightarrow \frac{1}{3}\times \frac{22}{7}\times (2.1{)}^2\times 8.4$

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

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

$\Rightarrow h=1.89cm$

Hence, the height of the smaller cones formed is $1.89cm$.