7. The radii of two cylinders are in the ratio 3 : 5 and their heights are in the ratio 2:3. Find the ratio of their volumes. 1) 14:9 2) 45 : 18 3) 15:18 4) 6:25.
Answers
Option (4)
Given :-
•The radii of two cylinders are in the ratio 3 : 5
•Their heights are in the ratio 2:3
To find :-
The ratio of their volumes
Solution :-
Given that
Ratio of the radii of two cylinders = 3:5
Let they be 3X units and 5X units
The radius of the first cylinder
(r) = 3X units
The radius of the second cylinder
(R) = 5X units
and
Ratio of the heights of the cinders = 2:3
Let they be 2Y units and 3Y units
The height of the first cylinder
(h) = 2Y units
The height of the second cylinder
(H) = 3Y units
We know that
Volume of a cylinder = πr²h cubic units
Volume of the first cylinder
= π×(3X)²×(2Y) cubic units
= π×9X²×2Y
= 18πX²Y cubic units
Volume of the second cylinder = πR²H cubic units
= π×(5X)²×(3Y) cubic units
= π×25X²×3Y
= 75πX²Y cubic units
The ratio of their volumes
= 18πX²Y : 75πX²Y
= 18πX²Y / 75πX²Y
= 18/75
= (6×3)/(25×3)
= 6/25
= 6:25
Answer :-
The ratio of the volumes of the two cylinders is 6:25
Used formulae:-
→Volume of a cylinder = πr²h cubic units
- π = 22/7
- r = radius
- h = height
→ a:b can be written as a/b
Answer:
The ratio of their volumes of 6:25
The correct option is is (d).
Step-by-step explanation:
As the radii of two cylinder in the ratio of 3:4
So the radius of first cylinder =3 r
and the radius of second cylinder = 5 r
Heights in the ratio =2:3
height of 1st cylinder =2 h
height of 2nd cylinder =3 h
ratio of volume=volume of 1st cylinder /volume of 2nd cylinder
V=π(3 r )² x 2 h/π(5 r)² x 3 h
V=18 rh/75 rh
V=6/25