Question

The volume of a cylinder is 40ft^3. Which expression represents the volume of a cone with the same base and height as the cylinder?
3(40)ft^3
3(1/40)ft^3
1/3(40)ft^3
1/3(40^2)ft^3

Answer 1

The third one, 1/3(40)ft^3, due to the fact that the volume of a cone is 1/3 that of a cylinder. This is shown from their formulas.
Cylinder
$\pi r^{2} h$
Cone
$\frac{ \pi r^{2} h}{3}$

Answer 2

Answer:

The volume of a cone is $\frac{1}{3}(40)\ ft^{3}$ .

Step-by-step explanation:

Formula

$Volume\ of\ a\ cylinder = \pi r^{2} h$

$Volume\ of\ a\ cone = \frac{1}{3} \pi r^{2} h$

Where r is the radius and h is the height .

As given

The volume of a cylinder is 40 ft ³ .

$40= \pi r^{2} h$

$Volume\ of\ a\ cone = \frac{1}{3}\times 40$

$Volume\ of\ a\ cone = \frac{1}{3}(40)\ ft^{3}$

Therefore the volume of a cone is $\frac{1}{3}(40)\ ft^{3}$ .