A cone and a cylinder have the same base radius and the same height. If the volume of the cone is 10 cubic units, what is the volume of the cylinder? (1 point) 30m cubic units 33TT cubic units 13π cubic units 3.33m cubic units.

Answer 1

To find the volume of the cylinder, we need to use the formula for the volume of a cone and the formula for the volume of a cylinder.

1. The volume \( V_c \) of a cone is given by the formula: \[ V_c = \frac{1}{3} \pi r^2 h \]

2. The volume \( V_{cy} \) of a cylinder is given by the formula: \[ V_{cy} = \pi r^2 h \]

Given that the volume of the cone is 10 cubic units: \[ V_c = \frac{1}{3} \pi r^2 h = 10 \]

From this, we can determine \( \pi r^2 h \): \[ \pi r^2 h = 3 \times 10 = 30 \]

Now, we can find the volume of the cylinder: \[ V_{cy} = \pi r^2 h = 30 \text{ cubic units} \]

Thus, the volume of the cylinder is 30 cubic units.