Question

A hollow sphere of external and internal diameters 4cm and 8 cm respectively.thr sphere is melted anf recast into the shape of cone whose radius is 8 cm find height of cone.​

Answer 1

Height of cone is 7 cm.

Step-by-step explanation:

As we already know that Volume of a Sphere of the radius (r) = $\frac {4}{3}\times{\pi}\times{r^3}$

In order to find Volume of Hollow Sphere of Outer and Inner radius ($r_{1}$) and ($r_{2}$) respectively =  

$\frac {4}{3}\times{\pi}\times{r_{1}^3} -   \frac {4}{3}\times{\pi}\times{r_{2}^3}$

$\frac {4\times\pi}{3}(r^{3}_{1} - r^{3}_{2})$

=$\frac {4\times\pi}{3}(8^{3} - 4^{3})$

=$\frac {4\times\pi}{3} (512 - 64)$

=$\frac {4\times\pi}{3} (448)$ ''''''(i)

As we know that the hollow sphere is melted to form Cone, which says that the Volume of Hollow Sphere will be equal to Volume of Cone

As per Question, Volume of Cone = The Equation (i)

$\frac{1}{3}\times\pi\times{R^{2}}\times{H} = \frac {4\times\pi}{3} (448)$

Solving the above equation Gives, H = 7 cm

Height of Cone is 7 cm.