find the curved surface area and volume of the cylinder formed by a rectangular sheet in the following conditions a rectangular sheet of dimension 21 cm by 14 cm taking the longest side as a hide a rectangular sheet of a dimension 21 cm by taking smallest side as a height
Answers
Answer:
A rectangular sheet of paper 30 cm×18 cm can be transformed into the curved surface of a right circular cylinder in two ways i.e., either by rolling the paper along its length or by rolling it along its breadth. Find the ratio of the volumes of the two cylinders thus formed.
Let V
1
and V
2
be the volumes of two cylinders. When the sheet is folded along its length, it forms a cylinder of height h
1
=18cm and perimeter of base equal to 30cm. Let r
1
be the radius of the base. Then,
2πr
1
=30⇒r
1
=
π
15
∴V
1
=πr
1
2
h
1
=π×
π
2
225
×18cm
3
=
π
225
×18cm
3
Similarly, V
2
=πr
2
2
h
2
=π×(
π
9
)
2
×30cm
3
=
π
81×30
cm
3
∴
V
2
V
1
=
81×30
225×18
=
3
5
.
Step-by-step explanation: