Question

A metal sphere of radius 12 cm
is melted and recast into 27
small spheres. What is the
radius of each sphere?​

Answer 1

Answer:

Since we have given that

Radius of metallic sphere = 12 cm

Radius of small cone = 4 cm

Height of small cone = 3 cm

So, Volume of metallic sphere is given by

\begin{lgathered}\frac{4}{3}\pi r^3\\\\=\frac{4}{3}\times \frac{22}{7}\times 12\times 12\times 12\end{lgathered}

3

4

πr

3

=

3

4

×

7

22

×12×12×12

And volume of cone is given by

\begin{lgathered}\frac{1}{3}\pi r^2h\\\\=\frac{1}{3}\times \frac{22}{7}\times 4\times 4\times 3\end{lgathered}

3

1

πr

2

h

=

3

1

×

7

22

×4×4×3

So, Number of cones so formed is given by

\begin{lgathered}\frac{\text{Volume of sphere}}{\text{Volume of cone}}\\\\=\frac{\frac{4}{3}\times \frac{22}{7}\times 12\times 12\times 12}{\frac{1}{3}\times \frac{22}{7}\times 4\times 4\times 3}\\\\=144\ cones\end{lgathered}

Volume of cone

Volume of sphere

=

3

1

×

7

22

×4×4×3

3

4

×

7

22

×12×12×12

=144 cones

Hence, there are 144 cones so formed.