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A cylinder and a cone have equal radii of their bases and equal heights. If their curved surface area are in the ratio 8:5, show that the radius of each is to the height of each as 3:4. |
Answer» Given :-
To Show :-
FORMULA used :-
Solution :-→ LET radius of cone & cylinder = r → Height of cone & cylinder = h . → slant height of cone = l A/q, → (CSA of cylinder) / (CSA of cone ) = 8/5 → (2 * π * r * h ) / ( π * r * l ) = 8/5 π & r will be CANCEL, → (2h / l) = 8/5 → h / l = 4/5 Squaring both sides , → (h/l)² = (4/5)² → h²/ l² = 16/25 Putting l² = (r² + h²) in LHS, → h²/(r² + h²) = 16/25 Cross - Multiply, → 25h² = 16(r² + h²) → 25h² = 16r² + 16h² → 25h² - 16h² = 16r² → 9h² = 16r² → r²/h² = 9/16 Square - root both sides , → r/h = 3/4. Hence, → r : h = 3 : 4. (Ans). |
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