A right circular cone is $3.6 c m$ high and radius of its base is $1.6 c m$ . It is melted and recast into a right circular cone with radius of its base as $1.2 c m$ . Find its height.

6.4 c m

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5.4 c m

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6.8 c m

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4.4 c m

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Solution

The correct option is A $6.4 c m$
Radius of first cone, $r_{1} = 1.6 c m$
and height of first cone, $h_{1} = 3.6 c m$ .
Radius of second cone, $r_{2} = 1.2 c m$
and height of second cone, $= h_{2} c m$ .
Now, volume of the first cone $=$ volume of second cone
$⟹$ $\frac{1}{3} π {r_{1}}^{2} h_{1} = \frac{1}{3} π {r_{2}}^{2} h_{2}$
$⟹$ ${(1.6)}^{2} \times 3.6 = {(1.2)}^{2} \times h_{2}$
$⟹$ $h_{2} = 6.4 c m$ .
Hence, option $A$ is correct.

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A right circular cone is 3.6 cm high and radius of its base is 1.6 cm. It is melted and recast into a right circular cone with radius of its base as 1.2 cm. Find its height.

The correct option is A 6.4 cmRadius of first cone, r1=1.6cmand height of first cone, h1=3.6cm.Radius of second cone, r2=1.2cmand height of second cone, =h2cm.Now, volume of the first cone=volume of second cone⟹ 13πr12h1=13πr22h2⟹(1.6)2×3.6=(1.2)2×h2⟹h2=6.4cm.Hence, option A is correct.

A right circular cone is $3.6 c m$ high and radius of its base is $1.6 c m$ . It is melted and recast into a right circular cone with radius of its base as $1.2 c m$ . Find its height.