Question

A cylinder and the cone have the same diameter of 10 inches. The height of the cone is twice the height of the cylinder, which is 8 inches. Find the volume of each figure (leave your answer in terms of π). Which one has the greater volume?

Answer 1

is cylinder=200 and cone 400pi/3 the cylinder has a great volume

Explanation:

Answer 2

`\bf \textit{volume of a cylinder}\\\\ V=\pi r^2h\qquad \begin{cases} h=height\\ r=radius=(diameter)/(2)\\ ---------\\ diameter=10\\ r=5 \end{cases}\implies V=\pi 5^2h \\\\\\ \boxed{V=25\pi h}\\\\ -----------------------------\\\\`


`\bf \textit{volume of a cone}\\\\ V=\cfrac{\pi r^2h}{3}\qquad \begin{cases} h=height\\ r=radius=(diameter)/(2)\\ ---------\\ diameter=10\\ r=5\\ h=2h\leftarrow twiced \end{cases}\implies V=\cfrac{\pi 5^2\cdot 2h}{3} \\\\\\ V=\cfrac{50\pi h}{3}\implies \boxed{V=\cfrac{50}{3}\pi h}`