The volume of a cylinder is 40 ft which expression represents the volume of O.C. one with the same base and height as the cylinder

The volume of a cylinder is 40 ft which expression represents the volume of a Cone with the same base and height as the cylinder?

3(40) ft³

3(1/40) ft³

1/3(40)ft³

1/3(40²) ft³

The expression  that represents the volume of a cone is (40) ft³

Step-by-step explanation:

To find the expression that represents  the volume of a cone with the same height and base as the cylinder, we will follow the steps below:

First write down the formula for calculating volume of a cone   and volume of a cylinder

volume of a cone = πr²h

volume of a cylinder = πr²h

If the base are the same, this implies they have the same radius,  and from the question, it states that they have the same height, hence;

volume of a cone = (volume of a cylinder)

from the question, the volume of the cylinder is 40 ft³

volume of a cone = (volume of a cylinder)

                              = (40) ft³

volume of a cone =   (40) ft³

Therefore the expression  that represents the volume of a cone is (40) ft³

56 Machines

Step-by-step explanation:

To solve this problem we need to use the rules of ratio and proportion.

We have:

84 Machines : 32 Days

x : 21 Days

Let x = number of machines required

84:32 can also be

x : 21 can also be

Now we can solve for x by first cross multiplying.

=

32x = (84)(21)

32x = 1764

Now to find for x, we have to divide both sides by 32

x = 55.125

Now since we cannot have 1/8th of a machine we round up to 56.

We need 56 machines to produce the same number of articles in 21 days.