Please Help!!This is another one of my daughter's weekly math problems and I have absolutely no idea how to figure it out, let alone explain it to her. So I will be (re)learning something I don't remember on this one as well. Please explain as simply as possible so that I get it. LOL TY!
A circular table has an area of 1256 squared (little 2 to upper right of 6) inches. The table opens in the middle to allow the addition of leaves. Each leaf is 12 inches wide and is rectangular in shape. How many leaves must be added to change the area of the table to 2696 squared (little 2 upper right) inches? Work backwards and remember these formulas:
Area of a rectangle = length X width
Area of a circle = Pi r(squared) -there is a small 2 above right of the r
She is to show the work and explain how to arrive at the answer.
Any insight and help would be greatly appreciated from both my 11 year old daughter and myself.
if figure skating where easy, they would call it hockey! O, and Dr. Pepper is the best drink ever.
Well you may have to do some drawing on this one. first take out a piece of paper. Draw a circle. lable that circle 1256 inches. Now next to that draw a rectangle. Lable that 12 inches wide. Now you must find how many more inches you need for the table to be 2696 inches. That awnser is 1440
Ok we next need to figure out the leanth and width of each leaf. We already know the width (12 in.) so that leaves the leanth. We can use common sense and say that it is the same leanth of the table. That means we need to figure out the leanth of the table. On this one we will work backwards. You have the equation A (area) = Pi r(squared). You need to put 1256 in for A ( i recommend writing this down as we go). Now you have 1256=Pi r(squared). Pi is the same as 3.14, so we are going to put that in for Pi. You now have the equation 1256=3.14r(squared). Now you need to figure out r. You need to move 3.14 to the other side of the equation, so you must divide 1256 by 3.14 to "undo" the opperation. Your new equation is 400= r(squared). Now you must "undo" the opperation squared. To do this take the square root of 400. This is 20. Now you have r=20. that is you radius. you must now multipy that by 2. Your leanth is now 40 inches.
Now we have the leanth and width of your leaf. It is 12x40. In order to find the area of that you need to multiply 12x40. Your area of the leaf is 480.
Ok now you need to see how many 480's there are in 1440 (this is how many more inches we need) . There are 3
In conclusion you need 3 leafs in order to have a table with an area of 2696 inches.
I hope this was helpful
By the way im an 8th grader in advanced math (Algerbra), So my awnser is most likly correct.
Dr. Pepper Lover- Thank you so much for your help. I've been out of school for a very long time, your explanation of the problem was extremely helpful to me in remembering. You did an excellent job in your explanation of the steps. Now I need explain to my 11 year old so that she can figure it and arrive at her own answer. A million THANK YOU'S!!! and a thumbs up!
Yes of corse. I hope your daughter understands. best of luck
Excellent interpretation of the question and explanation from Kelli.
The drawing is of 2 half circles separated, with some
rectangles of length equal to the diameter
inserted in the middle.
Here is how you could lay out your answer.
~~~~~~~~~~~~~~~~~~~~~~~~~
Let r be the radius of the circular area
pi r^2 (pi r squared) = 3.14 r^2 = 1256
r^2 = 400
r = 20 (inches)
Diameter, 40 inches, becomes length of each leaf.
Width is 12 so one leaf has area 480.
Let n be the number of leaves.
480n = 2696 - 1256 = 1440
n = 1440/480 = 3
Regards - Ian
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