17.A solid right circular cone of diameter 14cm and height 8cem is mel

1.	17.A solid right circular cone of diameter 14cm and height 8cem is melted to form a hollow sphere if theexternal diameter of the sphere is 10 cm , find the internal diameter of the sphere.w sphere if the
Answer» Diameter of cone=14 cmso, Radius of cone= 7cm Height of cone= 8cm ∴ Volume of cone= 1/3pir^2h =1/3pi498 cm^3 In Sphere, External Radius R=5cm Let, Internal Radius = r Volume of Sphere = External Volume- Internal Volume = 4/3piR^3-4/3pir^3 =4/3pi[R^3-r^3] =4/3pi[5^3-r^3] But During Conversion Volume Remains Same So, Volume of Sphere=Volume of Cone 4/3pi[125-r^3]= 1/3pi498 4[125-r^3]=498 [125-r^3]=492 r^3=125-98 r^3=27 so, r =3 cm Internal Radius= 3cm So, Internal Diameter=3*2= 6cm

17.A solid right circular cone of diameter 14cm and height 8cem is melted to form a hollow sphere if theexternal diameter of the sphere is 10 cm , find the internal diameter of the sphere.w sphere if the

Answer»

Diameter of cone=14 cmso, Radius of cone= 7cm Height of cone= 8cm

∴ Volume of cone= 1/3*pi*r^2*h =1/3*pi*49*8 cm^3

In Sphere, External Radius R=5cm Let, Internal Radius = r

Volume of Sphere = External Volume- Internal Volume = 4/3*pi*R^3-4/3*pi*r^3 =4/3*pi[R^3-r^3] =4/3*pi[5^3-r^3]

But During Conversion Volume Remains Same

So, Volume of Sphere=Volume of Cone 4/3*pi[125-r^3]= 1/3*pi*49*8 4[125-r^3]=49*8 [125-r^3]=49*2 r^3=125-98 r^3=27 so, r =3 cm

Internal Radius= 3cm So, Internal Diameter=3*2= 6cm