Step-by-step explanation:
We start with the formulas for the volumes of a cylinder and a cone.
Cylinder:
[tex] V_{cylinder} = \pi r^2 h [/tex]
Cone:
[tex] V_{cone} = \dfrac{1}{3} \pi r^2 h [/tex]
Now we calculate the two volumes.
Cylinder:
[tex] V_{cylinder} = \pi r^2 h [/tex]
[tex] V_{cylinder} = \pi \times (10~cm)^2 \times 9~cm [/tex]
[tex] V_{cylinder} = \pi \times 100~cm^2 \times 9~cm [/tex]
[tex] V_{cylinder} = 900 \pi~cm^3 [/tex]
Cone:
[tex] V_{cone} = \dfrac{1}{3} \pi \times (10~cm)^2 \times 9~cm [/tex]
[tex] V_{cone} = \dfrac{1}{3} \pi \times 100~cm^2 \times 9~cm [/tex]
[tex] V_{cone} = 300 \pi~cm^3 [/tex]
The volume of the cylinder is 900pi cm^3, and the volume of the cone is 300pi cm^3.
Now we divide the volume of the cylinder by the volume of the cone.
[tex] \dfrac{900 \pi~cm^3}{300 \pi~cm^3} = 3 [/tex]
Dividing the volume of the cylinder by the volume of the cone gives us 3, showing that the volume of the cylinder is 3 times the volume of the cone.
