Question

An ice-cream cone of radius r and height h is completely filled by two spherical scoopes of ice-cream. If radius of each spherical scoop is `r/2`, then h : 2r equals

Options

• 1 : 8

• 1 : 2

• 1 : 1

• 2 : 1

Answer 1

1 : 2

Explanation:

Given:

Radius of cone is r.

Radius of scoop `R = r/2`

According to the question:

Volume of cone = 2 × Volume of one scoop

`1/3 πr^2h = 2 xx (4/3 π (r/2)^3)`

`r^2h = 2 xx 4 xx r^3/8`

`r^2h = 8 xx r^3/8`

r²h = r³

h = r

The ratio h : 2r

`h/(2r) = r/(2r) = 1/2`