Question

Spherical ball of diameter 21cm is melted and recasted into cubes, each of side 1 cm. Find the number of cubes thus formed. [Use π=22/7]

Answer 1

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Answer 2

Step-by-step explanation:

Working out:

The above question belongs to Surface area and Volumes. We have to find the number of cubes formed by melting a speherical ball. All the necessary measurements are given like:

Diameter of speherical ball = 21 cm

Side of each cube = 1 cm

Taking π = 22/7

We need to find the number of cubes formed?

So, we can visualize that total volume of the all the cubes will be equal to the total volume of the speherical ball. Let's consider the number of cubes be n

Then,

Volume of spherical ball = n × Volume of cube

Now applying the formula, and plugging the values:

$\sf{ \longrightarrow{ \dfrac{4}{3} \pi {r}^{3} = n \times {side}^{3} }}$⟶

4 πr 3 =n×side 3

$\sf{ \longrightarrow{ \dfrac{4}{3} \times \dfrac{22}{7} \times \dfrac{21}{2} \times \dfrac{21}{2} \times \dfrac{21}{2} = n \times {1}^{3} }}$⟶

$\sf{ \longrightarrow{11 \times 21 \times 21 = n}}$

Flipping it,

$\sf{ \longrightarrow{n = \boxed{ \sf{4851 \: cubes}}}}$

So, the number of cubes formed by melting the spherical ball is 4851 cubes.