Question 148880
True or False. If the radius of a circle is doubled, the area increases by a factor of 4.
To answer this, you need to know the area of a circle is:
(pi)r^2
if you were to double the radius, it would be:
(pi)(r+2)^2
= (pi)(r+2)(r+2)
= (pi)(r^2+4r+4)
This increased the area by MORE than a factor of 4.
Anwer: False
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True or False. Increasing the radius of a circle by 10 inches, increases the circumference of the circle by 20 inches.
To answer this, you need to know the circumference of a circle is:
2(pi)r
Now, if we increase the radius by 10:
2(pi)(r+10)
= 2(pi)(r+10)
= 2(pi)(r+10)
= 2(pi)r+2(pi)10
= 2(pi)r+(pi)20
This increased the circumference by (pi)20.
Answer: False
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Find the perimeter of a region bounded on three sides by a rectangle with a length of 1000 ft and a width of 600 ft and bounded above by a semicirle with a radius of 300 ft. Use 3.14 as the approximation for ( Do not include the lower half of the semicircle in the perimeter)
A)3542 ft
B)3592 ft
C)3502 ft
D)3522 ft
Circumference of the semi-circle is:
(.5)2(pi)r
= (.5)2(3.14)300
= (.5)2(3.14)300
= 2(3.14)150
= 2(471)
= 942 ft
perimeter of the 3-sided rectangle:
1000+1000+600 = 2600 ft
total perimeter:
942 ft + 2600 ft = 3542 ft
Answer: A
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Find the perimeter of an equilateral triangle (all sides have equal lengths) with side lengths 4 mm 
There are three sides to a triangle, therefore the perimeter is the total of the lengths:
4+4+4 = 12 mm