Given that a cylinder has a volume of 1200cm^3, what is the volume of a cone that has the same height and same radius as the cylinder? explain your reasoning

cylinder:

πr^2h = 1200

cone:
1/3 πr^2h = 1/3 (1200) = 400

what is the volume of a right circular cone with a diameter of 21 centimeters and a height of 87 centimeter

a right cylinder with radius 4 cm

and height 3 cm
314 cu cm
a cone with radius 5 cm and
height 12 cm
160 cu cm
a pyramid with base area
16 sq cm and height 30 cm
48 cu cm
a pyramid with a square base of
length 3 cm and height 16 cm
150.72 cu cm
Pairs

Match each three-dimensional figure to its volume based on the given dimensions. (Assua right cylinder with radius 4 cm

and height 3 cm
314 cu cm
a cone with radius 5 cm and
height 12 cm
160 cu cm
a pyramid with base area
16 sq cm and height 30 cm
48 cu cm
a pyramid with a square base of
length 3 cm and height 16 cm
150.72 cu cm
Pairsme π = 3.14.)

To find the volume of the cone that has the same height and radius as the cylinder, we can use the formula for the volume of a cone, which is given by:

V_cone = (1/3) * π * r^2 * h

where V_cone is the volume of the cone, r is the radius, and h is the height.

Since the cylinder and cone have the same height and radius, we can use the following information:

- The volume of the cylinder is given as 1200 cm^3.
- The formula for the volume of a cylinder is given by V_cylinder = π * r^2 * h.

We need to equate the volume of the cone to the volume of the cylinder and solve for V_cone.

So, we have:

V_cylinder = V_cone

π * r^2 * h = (1/3) * π * r^2 * h

Dividing both sides of the equation by π and h:

r^2 = (1/3) * r^2

Simplifying:

1 = (1/3)

This is not possible as 1 cannot be equal to 1/3.

Therefore, it is not possible for a cone to have the same height and radius as a cylinder while also having a different volume.