Question

A cylinder has volume 78 cm3 . What is the volume of a cone with the same radius and height? A 26 cm3 B 39 cm3 C 156 cm3 D 234 cm3

Answer 1

Answer:

Option A - $26 \mathrm{cm}^{3}$

Step-by-step explanation:

Given: The volume of a cylinder = $78 \mathrm{cm}^{3}$

Let us substitute the volume of cylinder in the formula.

The formula for volume of a cone is $V=\frac{\pi r^{2} h}{3}$                    (1)

The formula for volume of a cylinder is $V=\pi r^{2} h$              (2)

Substituting $V=78$ in equation (2), we get,

$\begin{array}{c}{V=\pi r^{2} h} \\{78=\pi r^{2} h}\end{array}$

Given that the cone has the same radius and height of that of the cylinder, let us substitute $78=\pi r^{2} h$ in equation (1)

$\begin{array}{l}{V=\frac{\pi r^{2} h}{3}} \\{V=\frac{78}{3}} \\{V=26}\end{array}$

Thus, the volume of a cone with the same radius and height of a cylinder is $26 \mathrm{cm}^{3}$.