Consider a circle with an area of 25π square inches. If the circle were to be extruded to a height of twice the diameter, what would be the volume of the cylinder?

Answer 1

If 25π is area; the radius is 5.

Now the diameter is 2d=20; the radius is 10; the new area is 100π=314.15926.......... . The formula is r^2π.

As for volume; the length is needed.

If "extrude" is in reference to length; then the length is 20. The area is r^2πL=1570.79........

π=3.1415926...............

Answer 2

The volume of a right circular cylinder is given by V = πr²h. Notice that πr² is the area of the circle (which is the base of the cylinder). We need to find h which is twice the diameter of the circle.

First find the radius of the circle:

25π = πr², so r² = 25, which means the radius is 5. So the diameter is 10. Which means the height of the cylinder is 20. Plug the value of 20 into the formula for the volume of the cylinder: V = (25π)(20).

Answer 3

Hello Lorraine:

The formula of the are of a circle is π*r², where r is the radius.

If we know that the area is 25π = 5²*π, we know the radius is 5 inches, so we have:

D = 2*r

D = 10

H=2*D = 20 inches

The volume of the cylinder is the are of the circle times it's height:

V = H*A = 20*25π = 500π cubic inches