Question

a solid sphere made of copper has a diameter of 6 cm It is melted and recast into small spherical balls of diameter 2 cm each assuming that there is no wastage in the process find the number of small spherical balls obtained from the given sphere

Answer 1

Answer:

Number of small spherical balls made = 27

Step-by-step explanation:

Diameter of the larger sphere = 6 cm

So, radius of larger sphere = 3 cm

$\text{Volume of larger sphere = }\frac{4}{3}\times\pi\cdot r^3\\\\\implies\text{Volume of larger sphere = }\frac{4}{3}\times 3.14\times 3^3\\\\\implies \text{Volume of larger sphere = }113.04\thinspace{ cm^3}$

Now, the larger sphere is melted to form smaller spherical balls

Diameter of small spherical balls = 2 cm

So, Radius of small spherical balls = 1 cm

$\text{Volume of small spherical balls = }\frac{4}{3}\times\pi\cdot r^3\\\\\implies\text{Volume of small spherical balls = }\frac{4}{3}\times 3.14\times 1^3\\\\\implies \text{Volume of small spherical balls = }4.19\thinspace{ cm^3}$

Now, since the no amount is wasted in the process and let number of small spherical balls made be n. Then,

Volume of larger sphere = n × Volume of small spherical balls

113.04 = n × 4.19

$\implies n = \frac{113.04}{4.19}\\\\\implies n = 26.97\approx 27$

Hence, Number of small spherical balls made = 27

Answer 2

Answer:

27cm

Step-by-step explanation:

Here n(volume of one small sphere) =volume of large sphere

ie:4/3πR³/4/3πr³=R³/r³

ie:3³/1³=27/1

Therefore the number of small spherical ball made is 27