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.
Answers
Given : 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.
To find : Ratio of the volumes of the two cylinders thus formed.
Solution :
We have , dimension of rectangular sheet of paper = 30cm × 18cm
For Case : (1)
When paper is rolled along its length :
Then, 2πr1 = 30
r1 = 30/2π
r1 = 15/π cm
Height of cylinder , h1 = 18 cm
So, Volume of cylinder, V1 = πr1²h1
V1 = π × (15/π)² × 18
V1 = (225 × 18) /π cm³
For Case (2) :
When paper is rolled along its breadth :
Then 2πr = 18
r2 = 18/2π
r2 = 9/π cm
Height of cylinder , h2 = 30 cm
So, volume of cylinder , V2 = πr2²h2
V2 = π × (9/π)² × 30
V2 = (81 × 30)/π cm³
Now, Ratio of the volumes of the two cylinders thus formed = V1 : V2
V1 : V2 = (225 × 18) /π : (81 × 30)/π
V1 : V2 = (225 × 18)/(81 × 30) = 5/3
V1 : V2 = 5 : 3
Hence the ratio of the volumes of the two cylinders thus formed is 5 : 3.
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Some questions of this chapter :
Write the ratio of total surface area to the curved surface area of a cylinder of radius r and height h.
https://brainly.in/question/15912058
The height of a right circular cylinder is 10.5 m. Three times the sum of the areas of its two circular faces is twice the area of the curved surface. Find the volume of the cylinder.
https://brainly.in/question/15911802
Answer:
3:5
Step-by-step explanation:
explanation in the attachment
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