Question

Two right circular cones of dimensions $h=4.1cm,r=2.1cm$ and $h=4.3cm,r=2.1cm$ are melted to form a sphere of radius

• A. 2.5 cm
• B. 2.7 cm
• C. 2.1 cm
• D. 2 cm

Answer 1

The correct option is C 2.1 cm

Given that, Two right circular cones of dimensions h=4.1cm,r=2.1cm h=4.3cm,r=2.1cm and are melted to form a sphere .

Let, the radius of sphere =R

Now,

Volume of sphere =volume of 1^st cone +volume of 2^nd cone ,

$\frac{4}{3}\pi .R^3=\frac{1}{3}\pi {r_1}^2{h}_1+\frac{1}{3}\pi {r_2}^2{h}_2$

$4.R^3={r_1}^2{h}_1+{r_2}^2{h}_2$

$4R^3={\left(2.1\right)}^{2}4.1+{\left(2.1\right)}^{2}4.3$

$4R^3=8.4{\left(2.1\right)}^2$

$R^3=2.1{\left(2.1\right)}^2$

$R=2.1cm$

Hence, this is the answer.