Question

7. A sphere and a circular cylinder have the same radius, r, and the height of the cylinder is 2r. a. What is the ratio of the volumes of the solids? b. What is the ratio of the surface areas of the solids?

Answer 1

Answer: (a) 2 : 3

(b) 4 :1

Step-by-step explanation:

`\\`The Volume of a sphere is given as

`(4)/(3)`
`\pi`
`r^(3)` and the volume of a cylinder is given as
`\pi`
`r^(2)`h

`\\`The ration of their volume is the same as Volume of Sphere : Volume of Cylinder , which gives

`\\`
`(4)/(3)`
`\pi`
`r^(3)` :
`\pi`
`r^(2)`h

`\\`recall that they have the same radius and the height of the cylinder is 2r , taking this into consideration, we have

`\\`
`(4)/(3)`
`\pi`
`r^(3)` :
`\pi`
`r^(2)`(2r)

`\\`which gives 4 : 6 = 2 :3

`\\`(b) The area of a sphere is 4
`\pi`
`r^(2)` and the surface area of the circular cylinder is
`\pi`
`r^(2)`

`\\`The ratio then gives

`\\`4
`\pi`
`r^(2)` :
`\pi`
`r^(2)` ,which gives

`\\`4 : 1