Question

Two solid cylinders are $12cmand18cm$ in height. Their diameters are $12cmand16cm$ respectively. Both the cylinders are melted and the material is moulded into a solid right circular cone of height $33cm$. Find its diameter.

• A. $28cm$
• B. $20cm$
• C. $14cm$
• D. $24cm$

Answer 1

Answer: (D)

$24cm$

$Volumeofcone=Sumofvolumesoftwocylinders$

$\Rightarrow \frac{1}{3}\pi R^{2}H=\pi r_1^2{h}_1+\pi r_2^2{h}_2\Rightarrow \frac{1}{3}\pi \times R^2\times 33=\pi (6\times 6\times 12+8\times 8\times 18)$

$\Rightarrow 11R^2=432+1152\Rightarrow R^2=144\Rightarrow R=\sqrt{144}=12cm$

Therefore, diameter of cone is $12$$\times$ $2$ $=$ $24$cm.