Question

if radii of two cylinders are in the ratio 4:3 and their heights are in the ratio 5:6, find the ratio of their curved surface area.
answer step by step

Answer 1

Let r and R be the radii of first and second cylinders and h and H be their heights respectively.
Then,
r/R = 4/3
and h/H = 5/6
From question,
CSA of first cylinder/CSA of second cylinder
= (2×pi×r×h)/(2×pi×R×H)
=(r×h)/(R×H)
= (r/R)×(h/H)
= (4/3) × (5/6)
= 20/18
= 10/9
Therefore the ratio of their curved surface area (CSA) is 10:9

Answer 2

Step-by-step explanation:

Ratio in radii of two cylinders = 4 : 3

and ratio in their heights = 5 : 6

Let r1 and r2 be the radii and h1, h2 be their

Heights respectively.

∴ r1 : r2 = 4 : 3 and h1 : h2 = 5 : 6

∴ r1 = 4/3 and h1/h2 = 5/6

∴ Surface area of the first cylinder = 2 πr1h1

and area of second cylinder = 2πr2h2

2 πr1h1/2πr2h2 = (r1/r2 ) × h1/h2 = 4/3 × 5/6 = 20/18

= 10/9 = 10 : 9

∴ Ratio in their surface areas = 10 : 9