Question

Question #787a4

Answer 1

I have given an outline of the method you could use to solve each part of the question, and the answer I got at the end.

Explanation:

For part a:

As the volume of the two shapes is equal, we can equate those volume equations.
The ratio of the cone's height to its radius is `h/r`, so this is what you want to solve for.

I got `h/r=12`.

For part b:

Draw a pair of cylinders, and label them with the dimensions in terms of the small cylinder's radius.

The sum of the volumes is given to us, so we can form an equation in terms of the radius, and solve it for the radius, allowing us to give each cylinder's dimensions.

I got `r=3/88`

Answer 2

`h/r = 4/1`, which means that `h` is 4 times the `r`
`h:r`
`4:1`

Explanation:

The volume of sphere is given by the formula `V_s= 4/3pir^3`;
Thevolume of cone is given by the formula `V_c=h/3pir^2`.

The condition here is that `V` and `r` of both figures are equal. By equating the two formulas, the following can be derived:

`V_s=V_c`
`4/3pir^3`=`h/3pir^2`
where `r_s=r_c`
`4/cancel3cancel(pi)`r`=h/cancel3` `cancel(pi)`
`4r=h`
`h/r=4/1`
`h:r`
`4:1`