2 circles labeled Set A and Set B overlap. Set A contains 1, set B contains 3, and the overlap of the 2 circles contains 2. The
1 answer:
The region(s) represent the intersection of Set A and Set B (A∩B) is region II
<h3>How to determine which region(s) represent the intersection of Set A and Set B (A∩B)?</h3>The complete question is added as an attachment
The universal set is given as:
Set U
While the subsets are:
- Set A
- Set B
The intersection of set A and set B is the region that is common in set A and set B
From the attached figure, we have the region that is common in set A and set B to be region II
This means that
The intersection of set A and set B is the region II
Hence, the region(s) represent the intersection of Set A and Set B (A∩B) is region II
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The Halloween conical hat, with given height, circular base and brim
extension has the following calculated parameters;
Part a. The slant height is <u>18.2 inches</u>
Part b. The volume of the cone is in.³
Part c. The area of the brim, <em>A</em> = <u>36·π in.²</u>
Part d. The area of the brim is found by <u>subtracting the area of the base of the cone from the area covered by the perimeter of the brim</u>
Reasons:
Known parameters;
Height of the conical portion, h = 18 inches
Base circumference, C = 5·π inches
Part a. Slant height of the conical portion; Required
Solution:
The circumference of a circle, C = 2·π·r
Therefore;
Which gives;
Radius, r = 2.5 inches
According to Pythagoras's theorem, we have; s² = r² + h²
Where;
s = The slant height of the cone
s² = 2.5² + 18² = 330.25
s = √(330.25) ≈ 18.2
- The slant height, <em>s</em> ≈ <u>18.2 inches</u>
Part b. The measure in cubic inches of candy that exactly fills the conical portion of the hat is the volume of the cone.
Therefore;
- The volume of the cone, V =
·π in.³
Part c. The extension of the brim from the base of the cone = 4 inches
The radius of the brim, R = Radius of the base of the cone + 4 inches
∴ <em>R</em> = 2.5 inches + 4 inches = 6.5 inches
Area of the brim, <em>A</em> = Area of the 6.5 inch circle - Area of the circular base of the cone
∴ A = π × 6.5² - π × 2.5² = 36·π
- The area of the brim, <em>A</em> = <u>36·π in.²</u>
Part d. The procedure for solving the question in part c, is described as follows;
- The area of the brim can be found by finding the entire area of the circle formed by the perimeter of the brim, then subtracting the area of the base of the cone from that area.
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