Question

A cylinder and a cone have the same diameter: 8 inches. The height of the cylinder is 9 inches. The height of the cone is 18 inches.

Use π = 3.14.

What is the relationship between the volume of this cylinder and this cone? Explain your answer by determining the volume of each and comparing them. Show all your work.

Answer 1

`\bf \begin{array}{llll} \textit{volume of a cylinder}=V_(cy)=\pi r^2 h \\\\ \textit{volume of a cone}=V_(cn)=(\pi r^2 h)/(3) \end{array}\qquad \begin{cases} r=radius=(diameter)/(2)\\\ h=height \end{cases} \\\\\\  \\\\ V_(cy)=\pi r^2 h\quad \begin{cases} r=(diameter)/(2)=(8)/(2)=4 \\\\ h=9 \end{cases}\implies V_(cy)=\pi\cdot 4^2\cdot 9 \\\\\\ V_(cn)=(\pi r^2 h)/(3)\qquad \begin{cases} r=(diameter)/(2)=(8)/(2)=4 \\\\ h=18 \end{cases}\implies V_(cn)=(\pi \cdot 4^2\cdot 18)/(3)`


`\bf V_(cn)=\pi \cdot 4^2\cdot 6 \\\\ -----------------------------\\\\ \textit{their relationship will be }\cfrac{V_(cy)}{V_(cn)}\implies \cfrac{\pi\cdot 4^2\cdot 9}{\pi \cdot 4^2\cdot 6} \\\\ \cfrac{9}{6}\implies \cfrac{3}{2}`

Answer 2

The cone is 2 pie r. that means that the dimaeter is 8 pie

8 pie times 18 = 144

cylinder is 9x8= 72

i think

hope this helps

and you have to subtract cone from cylinder