The lateral surface area of a cylinder is equal to the curved surface area of a cone. If the radius be the same, find the ratio of the height of the cylinder to the slant height of the cone.
Answers
LSA of cylinder=2×pi×r×h, CSA of cone=pi×r×l, r of cylinder= r of cone, ratio= 2×pi×r×h/pi×r×l = 2:1.
Finding the surface area of a cone is to measure the radius of the circle part of the cone.
As well as the next step is to find the area of the circle, or base.
Even the area of a circle is 3.14 times the radius squared (πr2)
Lateral surface area of a cylinder = 2πrh
Make h the subject:
A = 2πrh
h = A/2πr
Curved surface area = πrl
Make l the subject:
A = πrl
l = A/πr
Find the ratio of the height of the cylinder to the slant height of the cone:
Given that the area and the radius are the same
Ratio = A/2πr : A/πr
Divide by A/πr:
Ratio = 1/2 : 1
Multiply by 2:
Ratio = 1 : 2
Answer: the ratio of the height of the cylinder to the slant height of the cone is 1: 2