Question

The height of a solid metal cylinder is $20cm$. Its radius is $1.5cm$. The cylinder is melted and cast into spheres of each of radius $1.5cm$. How many such spheres can be cast from the cylinder?

Answer 1

Given that:

$h=20cm,r$(for cylinder)$=1.5cm,R$(for sphere)$=1.5cm$

Solution:

Volume of cylinder$=\pi \times r^2\times h$

$=\frac{22}{7}\times (1.5{)}^2\times 20c{m}^3$

Volume of Sphere$\frac{4}{3}\times \pi r^3$

$=\frac{4}{3}\times \frac{22}{7}\times (1.5{)}^{3}c{m}^3$
When a solid of one shape is melted into another shape, the amount of volume remains the same.

Number of spheres cast from the cylinder $=\frac{\text{Volume of cylinder}}{\text{Volume of sphere}}$

$=\frac{\frac{22}{7}\times (1.5{)}^2\times 20c{m}^3}{\frac{4}{3}\times \frac{22}{7}\times (1.5{)}^{3}c{m}^3}$

$=\frac{3\times 20}{4\times 1.5}$

$=10$

So, number of spheres can be cast from cylinders $=10$