Twelve solid hemispheres of the same size are melted and recastto in a right circular cylinder of diameter 7 cm and height 28 cm. Whatis the radius of the hemispheres?

let radius of hemisphere be r cm.

volume of 1 hemisphere =$$\dfrac{2}{3}\pir^3$$

volume of 12 hemisphere =$$\times12\dfrac{2}{3}\pir^3$$

diameter of cylinder=7cm

radius of cylinder,R=3.5cm

height of cylinder,H=28cm 

volume of 12 hemisphere = volume of cylinder

$$\times12\dfrac{2}{3}\pir^3=\pi r^2h$$

$$8\times r^3=(3.5)^2\times28$$

$$r^3=\dfrac{\times3.5\times3.5\times28}{8}$$

$$r^3=\times3.5\times3.5\times3.5$$

$$r=3.5$$cm