Question

$\text{A metallic sphere of radius 10.5 cm is melted and then recast into small cones, each of radius 3.5 cm and heigh 3cm.The number of such cones}\left(a\right)21\left(b\right)63\left(c\right)126\left(d\right)130$

Answer 1

Solution:-
Volume of sphere = $\frac{4}{3}\pi r^3$
$=\frac{4}{3}\times \frac{22}{7}\times 10.5\times 10.5\times 10.5$
Volume of metallic sphere = 4851 cm³
Now,
Volume of one cone = $\frac{1}{3}\pi r^{2}h$
$=\frac{1}{3}\times \frac{22}{7}\times 3.5\times 3.5\times 3$
Volume of one cone = 38.5 cm³
Total number of cones = $\frac{\text{Volume of metallic sphere}}{\text{volume of one cone}}$
$=\frac{4851}{38.5}$
$=126cones$
Total number of cones can be formed is 126