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.