Question

the diameter of internal and external surfaces of a hollow hemisphere shell are 6cm and 12cm respectively .it is melted and recast into a solid cylinder of height 2cm .find the radius of the cylinder​

Answer 1

Recall:

$\text {Volume of a sphere} = \dfrac{4}{3} \pi r^3$

$\text {Volume of a hemisphere} = \dfrac{2}{3} \pi r^3$

$\text {Volume of a cylinder} = \pi r^2h$

Find the volume of the hemisphere with diameter 12 cm:

$\text {Volume of a hemisphere} = \dfrac{2}{3} \pi r^3$

$\text {Volume of a hemisphere} = \dfrac{2}{3} \pi (12 \div 2)^3$

$\text {Volume of a hemisphere} = 144\pi \text{ cm}^3$

Find the volume of the hemisphere with diameter 6 cm:

$\text {Volume of a hemisphere} = \dfrac{2}{3} \pi r^3$

$\text {Volume of a hemisphere} = \dfrac{2}{3} \pi (6 \div 2)^3$

$\text {Volume of a hemisphere} = 18\pi \text { cm}^3$

Find the volume of the hemisphere:

$\text {Volume of a hemisphere} = 144\pi - 18\pi$

$\text {Volume of a hemisphere} = 126\pi \text { cm}^3$

Find the height of the cylinder:

$\text {Volume of a cylinder} = \pi r^2h$

$\pi r^2(2) = 126\pi$

$r^2 = 63$

$r = 3\sqrt{7} \text {cm}$

Answer: The radius is 3√7 cm

Answer 2

Answer:

r(of Cyli.) = 22.4 cm

Step-by-step explanation:

Formula for the Volume of Hollow Hemisphere = 2/3 π (R³-[r(of hemi.)]³) & for Solid Cylinder = π[r(of cyli.]²h.

By equating the both equations we get,

=> 2/3 [(12)³-(6)³] = [r(of Cyli.)]²(2)

By simplifying we get, r(of Cyli.) as 22.4 cm.