I'll do the first three problems (numbers 15 through 17) to get you started.
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Problem 15
<h3>Answer:
21.98</h3>
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Explanation:
We cut the diameter in half to get the radius. We can think of cutting the 14 in half to get 7, ignoring the pi while we cut in half. Then after we do that, we tack the pi back on.
In short, 14pi cuts in half to 7pi.
Then we could see that 7*pi = 7*3.14 = 21.98
The radius is about 21.98 inches.
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Problem 16
<h3>Answer:
78.5</h3>
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Explanation:
We'll plug r = 5 into the area of a circle formula.
A = pi*r^2
A = 3.14*5^2
A = 78.5 square yards approximately
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Problem 17
<h3>Answer: 6</h3>
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Explanation:
We'll use the formula
C = pi*d
which is the formula that ties together the circumference C with the diameter d.
Plug in the given circumference C = 12pi and isolate d
C = pi*d
12pi = pi*d
12 = d .... divided both sides by pi, which cancels out
d = 12
The diameter is 12. Your step by step picture doesn't have to be this wordy, but I'm doing this to help show that the circumference like 12pi simply has the "pi" part erased to get the diameter. This allows a reader to quickly spot the diameter if given the circumference in this form. And it also allows to go from the diameter to the exact circumference without any calculator involved.
Once you get the diameter, you cut it in half to get the radius. Half of 12 is 6, so the radius is 6 cm.
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You could also have this as your steps
C = 2*pi*r
12pi = 2*pi*r
12 = 2r
2r = 12
r = 12/2
r = 6
which is an alternative way to see that the radius is 6 cm.
