Please show work And answer should be in A= In squared
1 answer:
Before we dive into the explanation, these shaded regions are called sectors.
To solve for the shaded regions, we must use this formula
Area of the shaded region 1 = (central angle/360)x
the area of a circle is pi x radius squared, so we are basically saying this chunk of the area of the circle is the area of the shaded region. The central area in this case is 72. Now we know what fraction of the circle is one of the shaded region, because it is the same fraction as the central angle to 360. All we have left to do is plug it in. (BTW, the shaded regions are equal because their central angles are the same, so all we have to do is solve for one and multiply it by two).
Area of shaded region 1 = (72/360) x pi x 100
= (72/18) x pi x 5
= (360/18) x pi
= 20
Area of all shaded regions = (area of shaded region 1) x 2
= 20 x 2
= 40
To solve for the shaded regions, we must use this formula
Area of the shaded region 1 = (central angle/360)x
the area of a circle is pi x radius squared, so we are basically saying this chunk of the area of the circle is the area of the shaded region. The central area in this case is 72. Now we know what fraction of the circle is one of the shaded region, because it is the same fraction as the central angle to 360. All we have left to do is plug it in. (BTW, the shaded regions are equal because their central angles are the same, so all we have to do is solve for one and multiply it by two).
Area of shaded region 1 = (72/360) x pi x 100
= (72/18) x pi x 5
= (360/18) x pi
= 20
Area of all shaded regions = (area of shaded region 1) x 2
= 20
= 40
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<u>Answer-</u> Length of the curve of intersection is 13.5191 sq.units
<u>Solution-</u>
As the equation of the cylinder is in rectangular for, so we have to convert it into parametric form with
x = cos t, y = 2 sin t (∵ 4x² + y² = 4 ⇒ 4cos²t + 4sin²t = 4, then it will satisfy the equation)
Then, substituting these values in the plane equation to get the z parameter,
cos t + 2sin t + z = 2
⇒ z = 2 - cos t - 2sin t
∴
As it is a full revolution around the original cylinder is from 0 to 2π, so we have to integrate from 0 to 2π
∴ Arc length
Now evaluating the integral using calculator,
