Question

solve the question.....!!!!!

Answer 1

Answer:

3 : 4

Step-by-step explanation:

Given that base, height of cylinder and cone are same.

Let radius of cylinder = radius of cone = r

Let height of cylinder = height of cone = h.

Now,

Given that ratio of their C.S.A is 8:5

⇒ (CSA of cylinder)/(CSA of cone) = 8/5

⇒ (2πrh)/(πrl) =8/5

⇒ 5h = 4l

⇒ 5h = 4(√h² + r²)

On Squaring both sides, we get

⇒ (5h)² = [4√h² + r²]²

⇒ 25h² = 16(h² + r²)

⇒ 25h² = 16h² + 16r²

⇒ 9h² = 16r²

⇒ r²/h² = 9/16

⇒ r/h = √9/16

⇒ r/h = 3/4

⇒ r : h = 3 : 4

Therefore, Ratio of radius and height will be 3 : 4

Hope it helps!

Answer 2

let the height and radius of cylinder and cone be of h and r units .
thus, CSA of cylinder/CSA of cone=8/5
2πrh/πrl=8/5
2h/l=8/5
2h/underroot h^2+r^2)
on solving that u will get r/h=3/4 (u can see in above picture)
hence proved.
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