A solid metallic sphere of radius 9 cm is melted and recast into a cone whose height is four times its base radius $(h = 4 r)$ .
Find the base radius $r$ of the cone (in cm).

Question

A solid metallic sphere of radius 9 cm is melted and recast into a cone whose height is four times its base radius (h = 4r). Find the base radius r of the cone (in cm).

Accepted Answer

9. Sphere V = 4/3π*9^3. Cone V = 1/3π*r^2*(4r) = 4/3π*r^3. Equate: 4/3π*9^3 = 4/3π*r^3 => r^3 = 9^3 => r = 9 cm.

A solid metallic sphere of radius 9 cm is melted and recast into a cone whose height is four times its base radius $(h = 4 r)$ .
Find the base radius $r$ of the cone (in cm).

Step-by-Step Solution

Master this chapter in 30 minutes a day.

More Class 10 Conversion of Solids practice

A solid metallic sphere of radius 9 cm is melted and recast into a cone whose height is four times its base radius (h=4r).Find the base radius r of the cone (in cm).

Step-by-Step Solution

Master this chapter in 30 minutes a day.

More Class 10 Conversion of Solids practice

A solid metallic sphere of radius 9 cm is melted and recast into a cone whose height is four times its base radius $(h = 4 r)$ .
Find the base radius $r$ of the cone (in cm).