Question

Hemispherical bowl of internal and external diameter 6 cm and 10cm respectively is my train from indore right circular cylinder of radiu 14 centimetre find the height of a cylinder

Answer 1

$\bold{HEMISPERICAL \: BOWL}$

When a sphere is cut from middle its divided into two parts known as hemispheres.

$\bold{VOLUME \: OF \: HEMISPHERE}$

$\huge \boxed{\bold{\dfrac{2}{3} \times \pi \times {R}^{3} - {r}^{3}}}$

External diameter = 10cm

Radius = $\dfrac{10}{2}$

Radius = 5cm

Internal diameter = 6 cm

Radius = $\dfrac{6}{2}$

Radius = 3cm

So, volume will be,

$\mathsf{\dfrac{2}{3} \times \pi \times {5}^{3} - {3}^{3}}$

$\boxed{\mathsf{VOLUME OF HEMISPHERE = 205.33 cm^{3}}}$

$\bold{VOLUME \: OF \: CYLINDER }$

$\huge \boxed{\mathsf{Volume \: of \: cylinder = \pi r^{2} h}}$

$\mathsf{Volume \: of \: cylinder = \dfrac{22}{7} 14 \times 14 \times h}}$

$\mathsf{Volume \: of \: cylinder =616 h }$

$\bold{ACCORDING \: TO \: QUESTION }$

The hemisphere is melted in right-angle cylinder

So ,

$\boxed{VOLUME \: OF \: HEMISPHERE = VOLUME \: OF \: CYLINDER }$

$\mathsf{2250 = 616 \times h}$

$\mathsf{ \dfrac{205.33}{616} = h}$

$\huge \boxed{ \mathsf{h = 0.333}}$

Answer 2

h =3

volume of hemisphere =volume of cylinder

2/3 pi (R^3-r^3) =pi r^2 (h)

2/3(5^3-3^3) =14^2 (h)

2/3(125-27)=196h

2/3(98)=196h

1/3(196) =196h

1/3=h