Question

Please help!

1. Find the volume for 5 different spheres by randomly choosing different radii.
Using the same radii values, find the volume of 5 cylinders where the height of the cylinder is the same as the diameter of the sphere.

Answer 1

Please, see the attached file.

Thanks.

Explanation:

Please, see the attached file.

Thanks.

Answer 2

`\begin{array}{ccc}\text{Radius}&\text{Volume of sphere}&\text{Volume of cylinder}\\&&\\1&(4)/(3)\pi &2\pi \\&&\\2&(32)/(3)\pi &16\pi \\&&\\3&36\pi &54\pi \\&&\\4&(256)/(3)\pi &128\pi \\&&\\5&(500)/(3)\pi &250\pi\end{array}`

Explanation:

Use formulas for the volumes:

`V_(sphere)=(4)/(3)\pi r^3,\\ \\V_(cylinder)=\pi r^2h=\pi r^2\cdot 2r=2\pi r^3.`

1. When r=1,

`V_(sphere)=(4)/(3)\pi\cdot 1^3=(4)/(3)\pi,\\ \\V_(cylinder)=2\pi \cdot 1^3=2\pi.`

2. When r=2,

`V_(sphere)=(4)/(3)\pi\cdot 2^3=(32)/(3)\pi,\\ \\V_(cylinder)=2\pi \cdot 2^3=16\pi.`

3. When r=3,

`V_(sphere)=(4)/(3)\pi\cdot 3^3=36\pi,\\ \\V_(cylinder)=2\pi \cdot 3^3=54\pi.`

4. When r=4,

`V_(sphere)=(4)/(3)\pi\cdot 4^3=(256)/(3)\pi,\\ \\V_(cylinder)=2\pi \cdot 4^3=128\pi.`

5. When r=5,

`V_(sphere)=(4)/(3)\pi\cdot 5^3=(500)/(3)\pi,\\ \\V_(cylinder)=2\pi \cdot 5^3=250\pi.`

Note that for all r,

`(V_(sphere))/(V_(cylinder))=((4)/(3)\pi r^3)/(2\pi r^3)=(2)/(3).`