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Sagot :
The Volume of the solid obtained by rotating the region bounded by the curves is 5 cm³.
Volume of a solid plain:
The volume of a solid is a measure of the space occupied by an object. It is measured by the number of unit cubes required to fill the solid.
Given in the question:
y = 2 - 1/2x
y = 0 , x = 1 and x = 2
As we know that:
[tex]\int\limits^2_1 {\pi (2 - \frac{1}{2}x - 0 })^2 \, dx[/tex] ------------------------------ (1)
Simplifying,
[tex]\pi \int\limits^2_1 {(2 - \frac{x}{2} )}^2 \, dx[/tex][tex]\pi \int\limits^2_1 {(4 - 2x + \frac{x^2}{4} )\, dx[/tex]
⇒ [tex]\pi \int\limits^2_1 {(4 - 2x + \frac{x^2}{4} )\, dx[/tex]
⇒ [tex]\pi [ 4x - x^2 + \frac{x^3}{12}]_1^2[/tex]
⇒ [tex]\pi [(8 - 4+ \frac{8}{12} ) - ( 4 - 1 + \frac{1}{12} )[/tex]
⇒ [tex]\pi (1 + \frac{7}{12})[/tex]
⇒ [tex]\frac{19\pi }{12}[/tex]
We can write 19π / 12 as
(19× 22/7 )÷ 12
= 209/ 42
= 4.97 ≈ 5 cm³
Therefore, the volume is 5 cm³
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