Question

a sphere is placed in a cylinder.It touches the top,bottom and the curved surface of the cylinder.If radius of the base of the cylinder is r.what is the ratio of the radii of the sphere and the cylinder? what is the ratio of the curved surface area of the cylinder and the surface area of the sphere? what is the ratio of the volume of the cylinder and the sphere?​

Answer 1

Answer:

1:1, 1:1 and 3:2

Step-by-step explanation:

as per the attachment provided

Answer 2

Find the ratio of the radius of the sphere to the cylinder:

The sphere touches the curved surface of the cylinder

⇒ The diameter of the sphere = diameter of the cylinder

⇒  Radius of the sphere : Radius of the cylinder = 1 : 1

Find the ratio of curved surface area of the cylinder to the surface area of the sphere:

$\text {area of the surface area of the sphere} = 4\pi r^2$

$\text {area of the curved surface area of the cylinder} = 2\pi rh$

$h = \text {diameter of the sphere}$

$h = 2r$

$\text {area of the curved surface area of the cylinder} = 4\pi r^2$

$\text{Ratio of the curved surface area of the cylinder : Sphere } = 4\pi r^2 : 4\pi r^2$

$\text{Ratio of the curved surface area of the cylinder : Sphere } = 1 : 1$

Find the ratio of Volume of the cylinder to the Volume of the sphere:

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

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

$\text {Volume of the cylinder }= 2\pi r^3 \text{ (Since h = 2r)}$

$\text {Ratio of the volume of the cylinder : volume of the sphere} = \dfrac{4}{3} \pi r^3 : 2\pi r^3$

$\text {Ratio of the volume of the cylinder : volume of the sphere} =\dfrac{3}{2} : 1$

$\text {Ratio of the volume of the cylinder : volume of the sphere} = 3 : 2$

Answer: (a) 1 : 1 (b) 1 : 1 (c) 3 : 2