two cylinders are of equal heights have their radius in the ratio 2:5 find the ratio of their lateral surface areas and their volumes.
Answers
Answer:
For cylinder, we have
base radius=r, height=h
∴S
1
=Curved surface=2πrh
For cone, we have
l=
r
2
+h
2
and, S
2
=πrl=πr
r
2
+h
2
We have,
S
2
S
1
=
5
8
⇒
πr
r
2
+h
2
2πrh
=
5
8
⇒
r
2
+h
2
2h
=
5
8
⇒
r
2
+h
2
4h
2
=
25
64
⇒25h
2
=16r
2
+16h
2
⇒9h
2
=16r
2
⇒3h=4r
⇒
h
r
=
4
3
.
Step-by-step explanation:
Answer:
ratio of lateral surface areas of two cylinders is 2:5
ratio of volumes of cylinders = 4: 25
Step-by-step explanation:
given that:
two cylinders have equal heights
ratio of their radii = 2:5
let radius of first cylinder is A;
radius of another cylinder is B;
so A:B = 2:5
lateral surface area = 2πrh
ratio of lateral surface areas of two cylinders is 2πAh : 2πBh
⇒ A:B = 2:5
ratio of lateral surface areas of two cylinders is 2:5
volume of a cylinder = πr²h
ratio of volumes of cylinders = πA²h : πB²h
⇒ 2² : 5²
⇒ 4: 25
ratio of volumes of cylinders = 4: 25