Mensuration-47

From Homeworkwiki

Jump to: navigation, search

A right circular cylinder and a right circular cone have equal bases and equal heights.
If their curved surfaces are in the ratio 8 : 5, show that the radius of their base is to their height as 3 : 4.

Solution: Let radius of each cone be r and height h. It is given that

Curved surface of cylinder / Curved surface of cone = 8 / 5

Therefore, 2 Π r h / Π r l = 8 / 5

=> 2h / l = 8 / 5

=> l = 10h / 8 = 5h / 4

Now l2 = h2 + r2

=> (5h/4)2 = h2 + r2

=> 25 h2 = 16 h2 + 16 r2

=> 9 h2 = 16 r2

=> h2 / r2 = 16 / 9

=> h / r = 4 / 3

=> r / h = 3 / 4

Therefore, the radius of their bases to their height = 3 : 4

Personal tools
McAfee SECURE sites help keep you safe from identity theft, credit card fraud, spyware, spam, viruses and online scams