Question

A metallic cylinder of radius 8 cm and height 6 cm is melted and converted into a right
cone of height 6 cm. Find the radius of the base of the cone.​

Answer 1

Answer:

The radius of base of Cone is 8√3 cm

Step-by-step explanation:

Total volume of metal remains same either it is in cylindrical shape or it is converted into conic shape

So,

Volume of Cylinder

$V = \pi {r}^{2} h = \pi \times {8}^{2} \times 6 = 384\pi$

Now, Volume of Cone

$V = (1 \div 3)\pi {r}^{2} h \\ = (1 \div 3) \times \pi \times {r}^{2} \times 6 = 2\pi {r}^{2} \\ V = 2\pi {r}^{2}$

Now equating volume of Cone with Volume of Cylinder

$2\pi {r}^{2} = 384\pi \\ {r}^{2} = 384\pi \div 2\pi \\ {r}^{2} = 192 \\ r = \sqrt{192} = 8 \sqrt{3}$

So, the radius of base of Cone is 8√3 cm