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Hello sir, The lateral surface of a cylinder is equal to the lateral surface of the cone.The radius of the cylinder is equal to the radius of the cone.What is the ratio of the height of the cylinder to that of the slant height of the cone? thank you
Asked by seeni2005 | 22 Nov, 2018, 04:55: PM
answered-by-expert Expert Answer
Let r and h are respectively radius and height of cylinder.
Let R and H are respectively radius and height of cone.
 
lateral surface area of cylinder = 2πrh ..................(1)
 
lateral surface area of cone = begin mathsize 12px style πR square root of straight R squared plus H squared end root end style ..........................(2)
where begin mathsize 12px style square root of straight R squared plus H squared end root end style is slant height of the cone
since radius of cylinder and cone are equal and lateral surfaces are also equal, if we equate (1) and (2), we get
 
begin mathsize 12px style fraction numerator h over denominator square root of R squared plus H squared end root end fraction space equals space 1 half end style
Answered by Thiyagarajan K | 23 Nov, 2018, 01:50: AM

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