Answer:
The volume of a cylinder = 78 \mathrm{cm}^{3}78cm3
Let us substitute the volume of cylinder in the formula.
The formula for volume of a cone is V=\frac{\pi r^{2} h}{3}V=3πr2h (1)
The formula for volume of a cylinder is V=\pi r^{2} hV=πr2h (2)
Substituting V=78V=78 in equation (2), we get,
\begin{gathered}\begin{array}{c}{V=\pi r^{2} h} \\{78=\pi r^{2} h}\end{array}\end{gathered}V=πr2h78=πr2h
Given that the cone has the same radius and height of that of the cylinder, let us substitute 78=\pi r^{2} h78=πr2h in equation (1)
\begin{gathered}\begin{array}{l}{V=\frac{\pi r^{2} h}{3}} \\{V=\frac{78}{3}} \\{V=26}\end{array}\end{gathered}V=3πr2hV=378V=26
Thus, the volume of a cone with the same radius and height of a cylinder is 26 \mathrm{cm}^{3}26cm3 .