Question

DUE SOON please need as much help as possible!!

questions are down below please explain how you got the answer!!
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Answer 1

Va=4r³π

Explanation:

Vb=(4/3)r³π, Vc=r²πh, h is the height of the cylindrical container.

h=12r.

So now the volume of the cylinder is:

Vc=r²π*12r=12r³π.

There are 6 balls so their total volume is:

6*Vb=6*(4/3)*r³*π=(24/3)*r³π=8r³π.

Now we subtract the volume of 6 balls from the volume of the cylinder to get the volume of air Va inside the cylinder:

Va=Vc-6*Vb=12r³π-8r³π=4r³π.

So the volume of air inside of the cylinder is Va=4r³π

Hope This Helps!

Answer 2

Volume of air = 4πr³ (units cubed)

Explanation:

`\boxed{\begin{minipage}{4 cm}\underline{Volume of a cylinder}\\\\$V=\pi r^2 h$\\\\where:\\ \phantom{ww}$\bullet$ $r$ is the radius. \\ \phantom{ww}$\bullet$ $h$ is the height.\\\end{minipage}}`
`\boxed{\begin{minipage}{4 cm}\underline{Volume of a sphere}\\\\$V=(4)/(3) \pi r^3$\\\\where:\\ \phantom{ww}$\bullet$ $r$ is the radius. \\ \phantom{ww}$\bullet$ $h$ is the height.\\\end{minipage}}`

Model the squash ball as a sphere.

Assuming the six squash balls are packaged in a cylindrical container where each ball is one on top of the other, the height of the container is 6 times the height of a squash ball.

The height of a squash ball is its diameter, which is twice its radius.

Therefore, the height of the cylinder is 12 times the radius of the squash ball, and the radius of the cylinder is the radius of the squash ball.

Therefore:

`\begin{aligned}\textsf{Volume of the cylinder}&=\pi r^2 \cdot 12 r\\&=12 \pi r^3\end{aligned}`

where r is the radius of the sphere (squash ball).

To find the volume of air inside the container, subtract 6 times the volume of a sphere from the volume of the cylinder.

`\begin{aligned}\textsf{Volume of air}&=\textsf{Volume of cylinder}-\textsf{6 volume of sphere}\\&=12\pi r^3-6\left((4)/(3) \pi r^3\right)\\&=12\pi r^3-8\pi r^3\\&=4\pi r^3\;\; \sf units \; cubed\end{aligned}`