Question

The radius of a solid metalic sphere is 10 CM. It is melted and recost in to small cones of height 10cm and base radius 5cm. find the number of small cone formed​

Answer 1

EXPLANATION.

Radius of the solid metallic sphere = 10cm.

It melted and recast into small cones of height = 10cm.

Base of the radius = 5cm.

As we know that,

⇒ Volume of sphere = 4/3πr³.

⇒ Volume of cone = 1/3πr²h.

⇒ Volume of sphere = volume of cone.

⇒ 4/3πr³ = 1/3πr²h.

Put the values in the equation, we get.

⇒ 4πr³ = πr²h x (y).

⇒ 4r³ = r²h x (y).

⇒ 4 x 10 x 10 x 10 = 5 x 5 x 10 x (y).

⇒ 4 x 10 x 10 = 25 x y.

⇒ 400 = 25 x y.

⇒ 400/25 = y.

⇒ 16 = y.

Number of small cone formed = 16.

Answer 2

Given :-

The radius of a solid metallic sphere is 10 CM. It is melted and recast in to small cones of height 10cm and base radius 5cm.

To Find :-

No. of small cone

Solution :-

We know that

$\mid \pmb{Volume_{sphere} = \dfrac{4}{3}\pi r^3}\mid$

4/3 × π × 10³

4π/3  × 1000

4000π/3

Now

$\mid \pmb{Volume_{cone}= \dfrac{1}{3} \pi r^2h}\mid$

1/3 × π × 5 × 5 × 10

1/3 × π × 250

250π/3

According to the question

No. of cone = (4000π/3)/(250π/3)

No. of cone = 4000/250

No. of cone = 16