The cylinder below has a volume of 785 Feet cubed, and the cone has a volume of 314 Feet cubed.
Which explains which figure has the greater height?
A.The cylinder has a greater height because the bases are the same, but the cylinder has a greater volume.
B.The cylinder has a greater height because the volume of the cylinder is greater than twice the volume of the cone.
C.The cone has a greater height because the bases are the same, but the volume of the cylinder is less than 3 times the volume of the cone.
D.The cone has a greater height because the bases are the same, but the volume of the cylinder is less than 4 times the volume of the cone.
A cylinder has a volume of 78.5 feet squared
A cone has a volume of 78.5 feet squared.
Answers
Given : The cylinder has a volume of 785 Feet cubed, and the cone has a volume of 314 Feet cubed . Base has same radius
To Find : Choose correct options regarding Their height
Solution:
Volume of cylinder = πr²h
r = radius of base of Cylinder
h = height of cylinder
Volume of cone = (1/3) πr²h
r = radius of base of Cone
h = height of cone
If radius of base & height are same
then Volume of cylinder = 3 Times the Volume of Cone
=> As radius of Base of cone & cylinder are same
hence their height would be equal if
Volume of Cylinder = 3 * Volume of cone
Volume of Cylinder = 785
3 * Volume of cone = 3 * 314 = 942
785 < 942
=> Volume of Cylinder < 3 * Volume of cone
Hence height of cylinder < height of cone
option C
The cone has a greater height because the bases are the same, but the volume of the cylinder is less than 3 times the volume of the cone.
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