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The answer to POTW #26 was posted as a comment to it. Please check to see if you got the correct answer of _________ (I am not telling you. You'll have to check the POTW #26 thread).
POTW #27 is below: (It has some great Grade 8 math curriculum connections!)
I understand, as I wrote above this question is a lot of Grade 8 curriculum (Pythagorean theorem and knowledge of circles). The POTW is selected for 7/8 content, so some may be more challenging than others. The POTW exists outside of your grade for Grade 7 math. The POTW is to extend and challenge students. That being said, to try a question you cannot understand, there are many strategies to undertake (i.e. ask a peer, look up tutorial support on youtube or khan academy, etc.)
So here is how u solve this (I got help from my uncle) so we need to find the area of a circle which is radius x pi, so to find the radius of the circle we need to find the diameter and half that is radius. and how do we find the diameter? ;) Well the diameter is the distance from one end of the circle to the other, so because this is a circle, ALL WE HAVE TO DO TO FIND THE DIAMETER IS FIND THE LENGTH OF HALF THE RECTANGLE ;) so we take the Pythagorean Theorem and find the diameter ;) each rectangle is 8m by 6m (24/3 = 8 18/3 = 6 (three is there because the rectangle is divided by three rows and columns) so basically 8 squared + 6 squared is 100 so that is the hypotenuse squared so what time's what equal's 100? 10! so the diameter is 10m and half of that is 5m so the radius of the circle is 5m Now to find the area we do r(squared) * pi ((5 x 5) x 3.141) which equals 78.525m squared so the circle is 78.525m squared 1/6 of the total backyard is 84m squared (28 * 18= 504/6 = 84) so since the pool is 78.525m squared the couple's plans be approved (that was fun after I figured out how to answer this:)
Your response really helped me understand the question Vivian, but you did make a small mistake in your calculations which made a big difference in your answer. The backyard's measurements are 24m by 18m, not 28m by 18m.
I did my work hard copy. My answer is most likely incorrect, but I don't think their plan will be approved. I found the area of the whole circle to be 126.5 m2 (most likely wrong), which is greater than 1/6 of the area of the backyard, 72 m2.
I did it hard copy, found that the plan would not be approved, as the area of the pool is 78.54 (approx.) which is larger than 1/6 of the backyard (72 m2 is 1/6).
First we need to find the area of the pool. The pool is a circle and to find the area of the circle its pi x radius squared. To find the radius you it is just half of the diameter. So first we need to find the diameter. The diameter of the circle is length of the diagonal of the middle of the rectangle. So to solve we can use the Pythagorean Theorem. First we must find the side lengths of the smaller rectangle. 24/3=8 18/3=6 The smaller rectangle is 8m by 6m. The hypotenuse squared should equal the other two side lengths squared added together. 8x8=64 6x6=36 64+36=100 The square root of 100 is 10. Therefore the diameter is equal to 10. To find the radius we must half the diameter. 10/2=5 Now that we know that the radius is 5 we are able to find the area of the pool. pi x 5 squared 5 x 5=25 pi x 25= 78.5398163397m Now we know the area of the pool we need to see is it will be approved. The whole backyard its 24 x 18. 24 x 18 = 432m For it to be approved it would be no larger than 1/6 of the backyard. 432/6=72 So 1/6 of the backyard is 72m. 78.5398163397<72 The pool would end up not being approved.
I completed hardcopy but got the following results:
The side lengths of 1/9 of 18x24 is 6x8 6, 8, 10 form a Pythagorean triple. 10 is the diameter of the circle 5 is the radius. the area of the circle is 78.5cm2 rounded 1/6 of the yard is 72cm2 Therefore this pool cannot be built in the yard.
I am sorry but this explanantion makes no sense to me, and I do not know how to find the are of a circle
ReplyDeleteI understand, as I wrote above this question is a lot of Grade 8 curriculum (Pythagorean theorem and knowledge of circles). The POTW is selected for 7/8 content, so some may be more challenging than others. The POTW exists outside of your grade for Grade 7 math. The POTW is to extend and challenge students. That being said, to try a question you cannot understand, there are many strategies to undertake (i.e. ask a peer, look up tutorial support on youtube or khan academy, etc.)
ReplyDeleteSo here is how u solve this (I got help from my uncle) so we need to find the area of a circle which is radius x pi, so to find the radius of the circle we need to find the diameter and half that is radius. and how do we find the diameter? ;)
ReplyDeleteWell the diameter is the distance from one end of the circle to the other, so because this is a circle, ALL WE HAVE TO DO TO FIND THE DIAMETER IS FIND THE LENGTH OF HALF THE RECTANGLE ;) so we take the Pythagorean Theorem and find the diameter ;)
each rectangle is 8m by 6m (24/3 = 8 18/3 = 6 (three is there because the rectangle is divided by three rows and columns) so basically 8 squared + 6 squared is 100 so that is the hypotenuse squared so what time's what equal's 100? 10! so the diameter is 10m and half of that is 5m so the radius of the circle is 5m
Now to find the area we do r(squared) * pi ((5 x 5) x 3.141) which equals 78.525m squared so the circle is 78.525m squared
1/6 of the total backyard is 84m squared (28 * 18= 504/6 = 84) so since the pool is 78.525m squared the couple's plans be approved
(that was fun after I figured out how to answer this:)
Ignore the Last part as I made a mistake:
Delete1/6 of the backyard is 72m squared and since the pool is 78.525m squared it won't be approved.
Your response really helped me understand the question Vivian, but you did make a small mistake in your calculations which made a big difference in your answer. The backyard's measurements are 24m by 18m, not 28m by 18m.
DeleteI did my work hard copy. My answer is most likely incorrect, but I don't think their plan will be approved. I found the area of the whole circle to be 126.5 m2 (most likely wrong), which is greater than 1/6 of the area of the backyard, 72 m2.
DeleteI did this hard copy
ReplyDeleteI did it hard copy, found that the plan would not be approved, as the area of the pool is 78.54 (approx.) which is larger than 1/6 of the backyard (72 m2 is 1/6).
ReplyDeleteFirst we need to find the area of the pool. The pool is a circle and to find the area of the circle its pi x radius squared. To find the radius you it is just half of the diameter. So first we need to find the diameter. The diameter of the circle is length of the diagonal of the middle of the rectangle. So to solve we can use the Pythagorean Theorem. First we must find the side lengths of the smaller rectangle.
ReplyDelete24/3=8
18/3=6
The smaller rectangle is 8m by 6m. The hypotenuse squared should equal the other two side lengths squared added together.
8x8=64
6x6=36
64+36=100
The square root of 100 is 10. Therefore the diameter is equal to 10. To find the radius we must half the diameter.
10/2=5
Now that we know that the radius is 5 we are able to find the area of the pool.
pi x 5 squared
5 x 5=25
pi x 25= 78.5398163397m
Now we know the area of the pool we need to see is it will be approved. The whole backyard its 24 x 18.
24 x 18 = 432m
For it to be approved it would be no larger than 1/6 of the backyard.
432/6=72
So 1/6 of the backyard is 72m.
78.5398163397<72
The pool would end up not being approved.
I completed hardcopy but got the following results:
ReplyDeleteThe side lengths of 1/9 of 18x24 is 6x8
6, 8, 10 form a Pythagorean triple.
10 is the diameter of the circle
5 is the radius.
the area of the circle is 78.5cm2 rounded
1/6 of the yard is 72cm2
Therefore this pool cannot be built in the yard.