Question

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

• A. 1.1 cm
• B. 2.5 cm
• C. 2.9 cm
• D. 1.9 cm

Answer 1

The correct option is D 1.9 cm

Given,
Height of cone, $H=8.4\text{cm}$
Radius of base, $R=2.1\text{cm}$

Hight of small cones, $h=?$
Radius of base of small cones, $r=1.4\text{cm}$


$\frac{1}{3}\pi R^{2}H=\frac{1}{3}\pi r^{2}h\times 10R^{2}H=r^{2}h\times 10(2.1{)}^2\times 8.4=(1.4{)}^2\times h\times 10h=\frac{2.1\times 2.1\times 8.4}{1.4\times 1.4\times 10}h=1.89\text{cm}\cong 1.9\text{cm}$

Height of the smaller cones is 1.89 cm.