Question

A hollow sphere of internal and external diameters 4cm and 8cm respectively is melted to a cone of base diameter 8cm. The height of the cone is.

Answer 1

Answer:

14 cm

Step-by-step explanation:

external diameter of sphere=8cm=

radius=4cm

internal diameter of sphere=4cm=radius 2cm

diameter of base of cone=8cm=radius=4cm

volume of cone= volume of the material in the sphere

1/3π(4)^2×h=4/3π( R^3-r^3)

16h=4(4^3-2^3)

h=4×56/16= 14cm

Answer 2

$\textbf{\underline{\underline{According\:to\:the\:Question}}}$

★External radius = 4cm

★Internal radius = 2cm

★Volume of Sphere :-

$\tt{\rightarrow\dfrac{4}{3}\pi (4^3 - 2^3)}$

$\tt{\rightarrow\dfrac{224\pi}{3}}$

★Radius of resulting cone = 4cm

★Volume of cone :-

$\tt{\rightarrow\dfrac{1}{3}\pi r^{2}h}$

$\tt{\rightarrow\dfrac{1}{3}\pi\times 4\times 4\times h}$

$\tt{\rightarrow\dfrac{16\pi h}{3}}$

$\tt{\rightarrow\dfrac{16\pi h}{3}=\dfrac{224\pi}{4}}$

$\tt{\rightarrow h=\dfrac{223}{3}\times\dfrac{3}{16}}$

= 14

★Therefore

★Height of cone is 14 cm