This math question is under the Solid Mensuration topic. Let us recap the formulas of the volume of both the cylinder and the cone. [tex]V_{cylinder}= \pi r^2h [/tex] [tex] V_{cone}= \frac{1}{3} \pi r^{2}h [/tex]
So if the volume of the cylinder is 32.25 inches, [tex]32.25=V_{cylinder} [/tex] Then, [tex]32.25= \pi r^2h [/tex]
So, to obtain the value of the volume of the cone is we simply multiply [tex] \frac{1}{3} [/tex] to both of the sides of the equation. [tex] \frac{1}{3} 32.25= \frac{1}{3} \pi r^2h [/tex] [tex] 10.75= \frac{1}{3} \pi r^2h [/tex] [tex]10.75=V_{cone} [/tex] [/tex] So its value if the radius and its height is the same as to the cylinder is 10.75 cubic inches.
