Question

A spherical solid material of radius 18cm is melted and recast into three small solid spherical spheres of different sizes.If the radii of two spheres are 2cm and 12cm.Find the radius of the third sphere.

Answer 1

Answer:

16 cm

Step-by-step explanation:

vol. of big sphere= 4/3$\pi$r^3

                           = 4/3$\pi$*18*18*18

                            = 24*324$\pi$

                             =7776$\pi$ cm^3

vol. of sphere 1 =4/3$\pi$*2^3

                         = 4/3*8$\pi$

                          = 32/3 $\pi$ cm^3

vol. of sphere 2 =4/3$\pi$*12^3

                           = 4/3*1728$\pi$

                            =2304$\pi$ cm^3

vol.of sphere 3= vol. of big sphere-(vol. of sphere 2 +vol. of sphere 1)

4/3$\pi r^3$=$\pi$[7776-(32/3+2304)]

4/3r^3=[23328-(320+6912)]/3

4r^3=16384

r^3=16384/4

r^3=4096

r=16 cm