Question

a solid right circular cone of diameter 14 cm and height 8 cm is melted to a sphere if the external diameter of sphere is 10 cm find internal diameter​

Answer 1

Answer:

For cone,

d=14cm,r=7cm

v. o. c=1/3*pie *r*r*h

v. o. c=1/3*pie*7*7*8

v. o. c=1/3*pie*392......(1)

for sphere, external diameter =10cm

external volume of sphere =4/3*pie*r*r*r

e. v. o. s=4/3*pie*125

volume of sphere =external v. o. s- i. v. o.s

v. o. s=4/3*pie*125-4/3*pie*r*r*r

v. o.s=4/3*pie(125-r*r*r)

volume of cone =volume of sphere

1/3*pie*392=4/3*pie(125-r*r*r)

392=4(125-r*r*r)

392/4=125-r*r*r

98=125-r*r*r

r*r*r=125-98

r*r*r=27

therefore, r=3 cm

diameter =6cm