Question

a hollow sphere which has internal and external diameters as 14cm and 16cm, respectively, is melted and recast into a cone with a height of 16cm.Find the diameter of the base​

Answer 1

Answer:

diameter of the base is 13cm

Answer 2

Step-by-step explanation:

$vol. \: \: of \: \: s.shell = \frac{4}{3} \pi( {R}^{3} - {r}^{3})$

$vol. \: \: of \: \: cone = \frac{1}{3} \pi {r}^{2} h$

$vol. \: \: of \: \: cone = vol. \: \: of \: \: s.shell$

$\frac{1}{3} \pi {r}^{2} h = \frac{4}{3} \pi( {R}^{3} - {r}^{3})$

${r}^{2} h = 4( {R}^{3} - {r}^{3} )$

${r}^{2} \times 16 = 4(4096 - 2744)$

${r}^{2} \times 4 = 1352$

${r}^{2} = 338$

$r = 18.38$

$Diameter \: of \: base = 2r$

$\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = 36.76$