A paper of dimensions 22 cm x 18 cm is folded in two different ways to form two cylinders. Find the ratio of the volumes of two cylinders.
Answers
Answer:
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
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Answer:
If the sheet is folded along its length it forms a cylinder of height h1 = 18cm and perimeter = 30cm Consider r1 as the radius and V1 as the volume So we get 2 πr1 = 30 It can be written as r1 = 30/2 π = 15/π We know that V1 = πr12h1 By substituting the values V1 = π × (15/π) 2 × 18 We get V1 = (225/ π) × 18 cm3 We know that If the sheet is folded along its breadth it forms a cylinder of height h2 = 30cm and perimeter 18cm Consider r2 as the radius and V2 as the volume So we get 2 πr2 = 18 It can be written as r2 = 18/2 π = 9/π We know that V2 = πr22h2 By substituting the values V2 = π × (9/π) 2 × 3 We get V2 = (81/ π) × 30 cm3 So we get V1/V2 = {(225/ π) × 18}/ {(81/ π) × 30)} On further calculation V1/V2 = (225 × 18)/ (81 × 30) We get V1/V2 = 5/3 We can write it as V1:V2 = 5:3 Therefore, the ratio of the volumes of the two cylinders thus formed is 5:3. ← Prev QuestionNext QuestRead more on Sarthaks.com - https://www.sarthaks.com/721531/rectangular-sheet-paper-transformed-curved-surface-right-circular-cylinder-ways-namely?show=721536#a721536