Question

Two right circular cones having same base radius of $2.1$ cm but heights $4.1$ cm and $4.3$ cm are melted and recast into a single sphere Find the radius of the sphere so formed

• A. $2.1$ cm
• B. $2$ cm
• C. $4.2$ cm
• D. $3.1$ cm

Answer 1

Answer: (A)

The correct option is A $2.1$ cm
Volume of the sphere
$\frac{4}{3}\pi R^3$=volumes of the cones of hights $h_1$ and $h_2$ with same radius r
$=\frac{1}{3}\pi r^2(h_1+h_2)$
$=\frac{1}{3}\times \pi \times {\left(2.1\right)}^2\times \left(8.4\right)$
$R^3=\frac{1}{4}\times {\left(2.1\right)}^2\times \left(8.4\right)$
$={\left(2.1\right)}^3$
or $R=2.1cm$