12. Find the area of shaded portion inD 11 cmC С13.5 cmAB15 cm
2 answers:
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Answer:
Step-by-step explanation:
We are given that curves y= is rotated about x=4 .
Given that y=0 and x=2
We have to find the volume V generated by rotating the region bounded by the curves with the help of method of cylindrical shells.
First we find the intersection point
Substitute y=0 then we get
0=
x=0
Hence, x changes from 0 to 2.
Radius =4-x
Height of cylinder =y=
Surface area of cylinder =
Volume V generated by the rotating curves
=
V=
V=
V=
V=
Hence, the volume V generated by rotating the region by the given curves about x =4=.
Hi :) I'm guessing the shaded region is the region inside the rectangle but outside the circle.
To solve this problem, you need to find the area of the rectangle and area of the circle. Then subtract the circle's area from the rectangle's.
Area of a rectangle: length × width
The problem already tells you the area of the rectangle, because it says it is an 11 × 11 rectangle.
(11)(11) = 121
Area of rectangle: 121 units²
Area of a circle:
Plug in 5 for the radius r.
= 78.5
Area of circle: 78.5 units²
Now subtract 78.5 from 121.
121 - 78.5 = 42.5
The area of the shaded region is 42.5 units².
To solve this problem, you need to find the area of the rectangle and area of the circle. Then subtract the circle's area from the rectangle's.
Area of a rectangle: length × width
The problem already tells you the area of the rectangle, because it says it is an 11 × 11 rectangle.
(11)(11) = 121
Area of rectangle: 121 units²
Area of a circle:
Plug in 5 for the radius r.
Area of circle: 78.5 units²
Now subtract 78.5 from 121.
121 - 78.5 = 42.5
The area of the shaded region is 42.5 units².