Answer:
Option A - [tex]26 \mathrm{cm}^{3}[/tex]
Step-by-step explanation:
Given: The volume of a cylinder = [tex]78 \mathrm{cm}^{3}[/tex]
Let us substitute the volume of cylinder in the formula.
The formula for volume of a cone is [tex]V=\frac{\pi r^{2} h}{3}[/tex] (1)
The formula for volume of a cylinder is [tex]V=\pi r^{2} h[/tex] (2)
Substituting [tex]V=78[/tex] in equation (2), we get,
[tex]\begin{array}{c}{V=\pi r^{2} h} \\{78=\pi r^{2} h}\end{array}[/tex]
Given that the cone has the same radius and height of that of the cylinder, let us substitute [tex]78=\pi r^{2} h[/tex] in equation (1)
[tex]\begin{array}{l}{V=\frac{\pi r^{2} h}{3}} \\{V=\frac{78}{3}} \\{V=26}\end{array}[/tex]
Thus, the volume of a cone with the same radius and height of a cylinder is [tex]26 \mathrm{cm}^{3}[/tex].
The volume of the cone is 26 cubic centimeters.
A cylinder has a volume of [tex]78 \;\rm{cm}^3[/tex].
We need to determine the volume of a cone with the same dimensions compared to a cylinder.
Now,
The formula for finding the volume of the cylinder is [tex]\pi r^2h[/tex].
The formula for finding the volume of the cone is [tex]\dfrac{1}{3}\pi r^2h[/tex].
Therefore, the volume of the cylinder is thrice the volume of the cone if we consider the same dimensions.
Thus,
[tex]\begin{aligned} 3 \times \rm{volume\;of\;the\;cone}&=78\;\rm{cm^3}\\&=26\;\rm{cm^3} \end{aligned}[/tex]
Hence, the volume of the cone is 26 cubic centimeters.
To know more about the cone, please refer to the link:
https://brainly.com/question/10670510
