The ratio of the heights of a cone and a cylinder is 2 : 1 and the ratio of the radii of their bases is 3:1 respectively. Find the ratio of their volumes. :
Please answer
Answers
6:1
Step-by-step explanation:
Solution :-
Given that
The ratio of the heights of a cone and a cylinder = 2:1
Let they be 2X and X units
The height of the cone (h1) = 2X units
The height of the cylinder (h2) = X units
The ratio of the radius of their base = 3:1
Let they be 3Y and Y units
The radius of the cone (r1) = 3Y units
The radius of the cylinder (r2) = Y units
We know that
Volume of a cone = (1/3)πr²h cubic units
Volume of a cone = (1/3)πr²h cubic unitsVolume of a cylinder = πr²h cubic units
Volume of the cone = (1/3)π×(r1)²×h1
=> V1 = (1/3)π×(3Y)²×2X cubic units
=> V1 = (1/3)×π×9Y²×2X
=> V1 = π×3Y²×2X
=> V1 = 6πXY² cubic units ------------(1)
Volume of the cylinder = π×(r2)²×h2
=> V2 = π×Y²×X cubic units
=> V2 = πXY² cubic units -------------(2)
Ratio of their volumes = V1 : V2
=> 6πXY² : πXY²
=> 6πXY² / πXY²
=> 6/1
=> 6:1
Therefore, V1:V2 = 6:1
Answer:-
The ratio of the cone and the cylinder is 6:1
Used formulae:-
→ Volume of a cone = (1/3)πr²h cubic units
→ Volume of a cylinder = πr²h cubic units
π = 22/7r = radiush = height
Answer:
The ratio of the heights of a cone and a cylinder is 2 : 1 and the ratio of the radii of their bases is 3:1 respectively. Find the ratio of their volumes. :
Step-by-step explanation: