At a zoo, the lion pen has a ring-shaped sidewalk around it. The outer edge of the sidewalk is a circle with a radius of 11 m. T
he inner edge of the sidewalk is a circle with a radius of 9 m. (a) Write and simplify an expression for the exact area of the sidewalk. (b) Find the approximate area of the sidewalk. Use 3.14 to approximate π.
1 answer:
The formula for finding area of a circle is 
.
Essentially, we have two circles here. One is a larger outer circle, and the other in a smaller inner circle. In order to find the area of the sidewalk, we must find the area of the outer circle, then find the are of the inner circle. After we find both areas, we subtract.
See attached image for process of finding area, and subtracting areas to find the final area of the sidewalk.
Essentially, we have two circles here. One is a larger outer circle, and the other in a smaller inner circle. In order to find the area of the sidewalk, we must find the area of the outer circle, then find the are of the inner circle. After we find both areas, we subtract.
See attached image for process of finding area, and subtracting areas to find the final area of the sidewalk.
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<em>An </em><em>apothem</em><em> is a line from the center of a regular polygon at right angles to any of its sides.</em>
<u>For part A</u>,
We want to find area of pentagon (5 sided figure) given apothem is 1.38 in and side length as 2 inch.
If we look at the picture shown (attached), we can see that a triangle is formed. What is the area of this triangle?
square inches
<u><em>How many such triangles are there in a pentagon? 10. So we multiply 0.69 by 10 to get total area of pentagon.</em></u>
Area of Pentagon = square inches.
<u>For part B</u>,
We want to find area of hexagon (6 sided figure) given apothem is 1.73 in and side length as 2 inch.
If we look at the picture shown (attached), we can see that a triangle is formed. What is the area of this triangle?
square inches
<em><u>How many such triangles are there in a hexagon? 12. So we multiply 0.865 by 12 to get total area of hexagon.</u></em>
Area of Hexagon = square inches.
ANSWER:
Area of Pentagon is 6.9 square inches.
Area of Hexagon is 10.4 square inches.
Answer: 0.6827
Step-by-step explanation:
Given : Mean IQ score :
Standard deviation :
We assume that adults have IQ scores that are normally distributed .
Let x be the random variable that represents the IQ score of adults .
z-score :
For x= 90
For x= 120
By using the standard normal distribution table , we have
The p-value :
Hence, the probability that a randomly selected adult has an IQ between 90 and 120 =0.6827