Question

The base radius of solid in the form of a cone is 4 cm and the height of the cone is 9 cm. it is melted recast into spherical balls of radius 0.5 cm. Find the number of balls, thus obtained.​

Answer 1

Step-by-step explanation:

n * volume of sphere = volume of cone

therefore n=volume of cone /volume of sphere.

Answer 2

Number of balls can obtained is 287

Given:

The base radius of a cone r = 4 cm

The height of the cone h = 9 cm

The cone is melted recast into spherical balls

The radius of spherical ball 0.5 cm

To find:

Number of spherical ball

Solution:

Given radius of cone r = 4 cm

height of cone h = 9 cm

Volume of cone = (1/3) πr²h cm³

= $\frac{1}{3} (\frac{22}{7} )(4^{2} )9$ = 150.796  

Here, the volume of melted cone = 150.796 cm³

Given radius of small spherical ball  = 0.5 cm

Volume of  one small spherical ball =  4/3 πr³

= $\frac{4}{3} (\frac{22}{7} ) (0.5)^{3}$ = 0.524 cm³

Let "n" number of spherical balls are formed from melted cone

Then volume of n spherical balls = n(0.524)

As we know volume of melted cone = 150.796 cm³

⇒  n(0.524) cm³ = 150.796 cm³

⇒ n = 150.796/ 0.524 = 287.77

Therefore, number of balls can obtained = 287

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