Question

a cone is 8.4 cm high and the radius os its base is 2.1 cm it is melted and recast into a sphere . find the radius of sphere

Answer 1

let the radius and height of cone be r and h respectively
let the radius of cone be R
since the cone is recast into sphere therefore
vol of cone = vol of sphere
1/3pir^2h=4/3piR^3
r^2h=4R^3
(2.1)^2(8.4)=4R^3
4.41(8.4)=4R^3
4.41(2.1)=R^3
R=2.1cm
therefore required radius of sphere is 2.1cm

hope thus helps:p

Answer 2

vol. of cone = vol. of sphere

therefore

1/3 *pi*2.1*2.1*8.4=4/3 *pi *radius of sphere (r) raised to3

which implies 2.1*2.1*8.4*3 / 4*3=r^3

therefore r=2.1cm