A metallic cylinder of radius 8 cm and height 2 cm is melted and converted into a right circular cone of height 6 cm.

Question:

A metallic cylinder of radius 8 cm and height 2 cm is melted and converted into a right circular cone of height 6 cm. The radius of the base of this cone is
(a) 4 cm
(b) 5 cm
(c) 6 cm
(d) 8 cm

 

Solution:

(d) 8 cm
Radius of the cylinder = 8 cm
Height of the cylinder = 2 cm
Height of the cone = 6 cm

Volume of the cylinder  = Volume of the cone
Therefore,

$\pi \times 8 \times 8 \times 2=\frac{1}{3} \pi \times r^{2} \times 6$

$\Rightarrow 128=r^{2} \times 2$

$\Rightarrow r^{2}=\frac{128}{2}$

$\Rightarrow r^{2}=64$

$\Rightarrow r=8 \mathrm{~cm}$

Hence, the radius of the base of the cone is 8 cm.

 

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