SOLUTION: I'am an online student and I have the following Questions True or False. If the radius of a circle is doubled, the area increases by a factor of 4. True or False. Increas

Question 148880: I'am an online student and I have the following Questions

True or False. If the radius of a circle is doubled, the area increases by a factor of 4.

True or False. Increasing the radius of a circle by 10 inches, increases the circumference of the circle by 20 inches.

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
Find the perimeter of an equilateral triangle (all sides have equal lengths) with side lengths 4 mm

Answer by nerdybill(7384) (Show Source): You can put this solution on YOUR website!
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
.
*******************************************************
.
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

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