the CSA of cylinder is 264m² and it's volume is 924 m³.find the ratio of its diameter and it's height
Answers
Solution :-
Let us Assume that, Diameter of cylinder is D and height of cylinder is H .
Than,
→ CSA of cylinder = 2 * π * radius * Height
Putting values we get,
→ 2 * (22/7) * (D/2) * H = 264
→ 22 * D * H = 264 * 7
→ D * H = 12 * 7
→ DH = 84 ----------- Eqn(1)
Now,
→ Volume of cylinder = π * (radius)² * Height
Putting values we get,
→ (22/7) * (D/2)² * H = 924
→ 11 * D² * H = 924 * 2 * 7
→ D² * H = 84 * 14
→ (DH) * D = 84 * 14
Putting value of Eqn(1) now,
→ 84 * D = 84 * 14
→ D = 14 .
Putting Value of D in Eqn(1) again,
→ 14 * H = 84
→ H = 6 .
Therefore,
→ Ratio of Diameter : Height = 14 : 6 = 7 : 3 (Ans.)
Answer:
7:3
Step-by-step explanation:
CSA of cylinder = 2πrh
2πrh=264
rh = 264 x 7/22x2
rh= 42
h=42/r
volume of cylinder = πr²h
πr²h = 924
22/7 x r x r x 42/r= 924
r = 924 x 7 /(22 x 42)
r = 7
h =42/7=6
diameter = 14
diameter : height = 14:6
7:3
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