# Mensuration-47

### From Homeworkwiki

**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 l^{2} = h^{2} + r^{2}

=> (5h/4)^{2} = h^{2} + r^{2}

=> 25 h^{2} = 16 h^{2} + 16 r^{2}

=> 9 h^{2} = 16 r^{2}

=> h^{2} / r^{2} = 16 / 9

=> h / r = 4 / 3

=> r / h = 3 / 4

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