Question

Two right circular cones of dimensions h=4.1, r=2.1 cm and h = 4.3 cm, r = 2.1 cm 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 dimension of two right circular cone are h=4.1,r=2.1 and h=4.3 ,r=2.1 volume of first right circular cone=$\frac{1}{3}\pi \left(2.1{)}^2\right(4.1)=\frac{\pi }{3}18.081$

And volume of second right circular cone=$\frac{1}{3}\pi (2.1)^{2}(4.

3)=\frac{\pi }{3}18.963$

Then total volume of two right circular cone =$\frac{\pi }{3}18.081+\frac{\pi }{3}18.963=\frac{\pi }{3}\left(37.044\right)=12.348\pi$

Let R is the radius of new sphere made by melted cones

So $\frac{4}{3}\pi R^3=12.348\pi \Rightarrow R^3=\frac{12.348\times 3}{4}=9.261\Rightarrow R=2.1cm$