A sheet of length I metres and height h metres is rolled to form a cylinder of height h metres and diameter d metres. The opposite edges coincide exactly without any overlap.) What is the length (1) of the sheet in terms of d?
Answers
Step-by-step explanation:
If the sheet is rolled along its length then the circumference will be equal to the length of the rectangle.
∴2πr=44
∴r=
2×
7
22
44
∴r=7 cm
Also, height of the cylinder will be equal to the breadth of the rectangle.
∴h=18 cm
∴ volume of the cylinder =πr
2
h
=
7
22
×7
2
×18
=2772 cm
3
Answer:
Using the calculation for the circumference of a circle, C = d, we can calculate the length of the sheet in terms of the cylinder's width. The sheet's length will be the same as the cylinder's diameter.
To determine the extent of the sheet, we can use Pythagoras' equation. Let's refer to the sheet's length as L.
We have a right-angled triangle with the sheet's length as the hypotenuse, the cylinder's diameter as the base, and the cylinder's height as the height.
Using Pythagoras' theorem, we can write:
L² = h² + (d/2)²
L² = h² + d²/4
L = √(h² + d²/4)
Now we can substitute the value of h in terms of d. Since the height of the cylinder is h, we know that the length of the sheet is equal to the circumference of the cylinder, which is πd.
Therefore, we can write:
πd = √(h² + d²/4)
πd² = h² + d²/4
h² = πd² - d²/4
h² = (4π-1)/4 * d²
h = √((4π-1)/4) * d
Now we can substitute the value of h in the equation for L:
L = √(h² + d²/4)
L = √(((4π-1)/4)d² + d²/4)
L = √((4π-1)/4 + 1/4) * d²
L = √(4π/4) * d
L = √π * d
Therefore, the length of the sheet in terms of the diameter of the cylinder is √π times the diameter of the cylinder.
Learn more about Pythagoras' equation :
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