The radii of two right circular cylinders are in the ratio 2:3 and
their heights are in the ratio 5:4. Calculate the ratio of their
curved surface areas and also the ratio of their volumes.
Answers
Step-by-step explanation:
Given :-
The radii of two right circular cylinders are in the ratio 2:3 and their heights are in the ratio 5:4.
To find :-
Calculate the ratio of their curved surface areas and also the ratio of their volumes ?
Solution:-
Given that
The ratio of the radii of two right circular cylinders = 2:3
Let they be 2X and 3X units
The radius of the first cylinder (r1)= 2X units
The radius of the second cylinder (r2) = 3X units
The ratio of the heights of the two right circular cylinders = 5:4
Let they be 5X and 4X units
The height of the first cylinder (h1) = 5Y units
The height of the second cylinder (h2) = 4Y units
We know that
Curved Surface Area of the cylinder
= 2πrh sq.units
Curved Surface Area of the first cylinder
=> A1 = 2π(2X)(5Y) sq.units
=> A1 = 20πXY sq.units ---------(1)
Curved Surface Area of the second cylinder
=> A2 = 2π(3X)(4Y) sq.units
=> A2 = 24πXY sq.units ---------(2)
The ratio of the CSA's of two cylinders
=> A1:A2
=> 20πXY : 24πXY
=> 20πXY / 24πXY
=> 20/24
=> 5/6
=> 5:6
=> A1:A2 = 5:6
And
We know that
Volume of a cylinder (V) = πr²h cubic units
Volume of the first cylinder (V1)
=> V1 = π(2X)²(5Y) cubic units
=> V1 = π(4X²)(5Y)
=> V1 = 20πX²Y cubic units
Volume of the second cylinder (V2)
=> V2 = π(3X)²(4Y) cubic units
=> V2 = π(9X²)(4Y)
=> V2 = 36πX²Y cubic units
The ratio of their volumes
=> V1:V2
=> 20πX²Y : 36πX²Y
=> 20πX²Y / 36πX²Y
=> 20/36
=> 5/9
=> 5:9
V1:V2 = 5:9
Answer:-
The ratio of the Curved Surface Areas of two right circular cylinders = 5:6
The ratio of the Curved Surface Areas of two right circular cylinders = 5:9
Used formulae:-
- Curved Surface Area of the cylinder
- = 2πrh sq.units
- Volume of a cylinder (V) = πr²h cubic units
- r = Radius
- h =height
- π=22/7