If a solid right circular cone of height r unit is made by melting a solid sphere of radius r unit . Then the radius of the base of the cone will be

Options

A. 2r unit
B. 3r unit
C. r unit
D. 4r unit

Answer

A

Explanation

Radius of the sphere = r unit
` :.` Volume of the sphere ` = 4/3 pir^(3) ` cubic - unit
Also , the height of the cone
Let the radius of the base of the cone be `r_(1)` unit
` :. ` Let the radius of the base ` = r_(1)` unit
` :. ` Let the radius of the base = ` r_(1)` unit
` :. ` the volume of the cone ` = 1/3 pir_(1)^(2) xx r ` cubic - unit
As per question , ` 1/3 pir_(1)^(2) xx r = 4/3 pir^(3) `
` rArr r_(1)^(2) = 4r^(2) rArr r_(1)^(2) = (2r)^(2) rArr r_(1) = 2r`
` :. ` radius of the cone = 2r unit
Hence (a ) is correct