Question

PLEASE HELP ME i would really appreciate it

Answer 1

`h=(24)/(\pi)\approx7.64`

Explanation:

we are given that the cube and cylinder have the same volume. we shall use the formulae for volume of cube and cylinder:

`V_(cube)=a^3` where a is the length of an edge.

`V_(cyl)=\pi r^2 h` where r is the radius of the circular base, and h is the height of the cylinder.

first find the volume of the cube:

`V_(cube)=6^3=2^3* 3^3`.

next, the volume of the cylinder. note that 6 is the diameter, so 3 is the radius.

`V_(cyl)=3^2\pi h`

now, these two are equal. we have

`2^3*3^3=3^2\pi h`

dividing both sides by
`3^2`, we have

`2^3* 3=\pi h \implies 24=\pi h`

and finally, we have

`h=(24)/(\pi)`

Answer 2

Height= 7.64 cm

Explanation:

The volume
`\sf V` of a cube is given by the formula
`\sf V_{\textsf{cube}} = s^3`, where
`\sf s` is the length of a side of the cube.

The volume
`\sf V` of a cylinder is given by the formula
`\sf V_{\textsf{cylinder}} = \pi r^2 h`, where
`\sf r` is the radius of the base and
`\sf h` is the height of the cylinder.

Given:

- Length of the cube (
`\sf s`) = 6 cm

- Diameter of the cylinder (
`\sf d`) = 6 cm (the radius
`\sf r` is half of the diameter)

First, find the volume of the cube:

`\sf V_{\textsf{cube}} = s^3 = 6^3 = 216 \, \textsf{cm}^3`

Now, find the radius of the cylinder (
`\sf r`):

`\sf r = (d)/(2) = (6)/(2) = 3 \, \textsf{cm}`

Since the cube and the cylinder have the same volume:

`\sf V_{\textsf{cube}} = V_{\textsf{cylinder}}`

`\sf 216 = \pi \cdot 3^2 \cdot h`

Solve for the height (
`\sf h`) of the cylinder:

`\sf h = (216)/(\pi \cdot 3^2)`

`\sf h = (216)/(\pi \cdot 9)`

`\sf h = (216)/(28.27433388)`

`\sf h \approx 7.639437268 \, \textsf{cm}`

Therefore, the height of the cylinder is approximately
`\sf 7.64 \, \textsf{cm}` in the nearest hundredth.