Question

76. A solid metalic cone of radius 2cm and height 8cm is melted
into a sphere. Find the radius of sphere.​

Answer 1

$\mathfrak \pink{hello \: friend}$

We know that,

When a solid is converted into another solid by melting, it's volume will remain constant.

Therefore,

Volume of cone= Volume of sphere

1/3πr²h=4/3πr³

1/3×22/7×2×2×8=4/3πr³

704/21= 4/3πr³

704/21×3/4×7/22= r³

176÷22= r³

8= r³

r= 2 cm

Answer=>2 cm

Answer 2

$\underline\bold{Answer}$

The radius of solid metallic cone is 2 cm.

Height of the metallic cone is 8 cm.

Let the radius of sphere be R.

Volume of cone = Volume of sphere

$\bold{ \frac{1}{3} \pi {r}^{2} h = \frac{4}{3} \pi {R}^{3}}$

$\bold{ \frac{1}{3} \pi \: 2 \times 2 \times 8 = \frac{4}{3} \pi {R}^{3} }$

$\bold{ {R}^{3} = \frac{2 \times 2 \times 8}{4}} \\ {R}^{3} = \frac{32}{4} \\ {R}^{3} = 8 \\ {R} = 2 \: cm$

∴ The radius of sphere is 2 cm.