Question

Audrey has a recipe for bar cookies that calls for a 9" x 13" pan. However, she wants to make them in a round pan so she can cut into wedges instead of bars. a) find area of original pan. b) find the radius of a circular pan that would provide that same area. Round to nearest inch. c) Find the area of one cookie wedge if its central angle measures 15 degrees. Round to nearest square inch.

Answer 1

please help! I have test!

Answer 2

A. Assume we're in a 2D world and use the following equation to calculate the area of the pan:
Area = Length x Width

Answer 3

a) the area is 117 inches.
But I don't understand the rest.

Answer 4

Correct. Now, part B.

B. Use the area calculated in part A to solve the following equation for the radius:
\[Area = \pi * radius^2\]
Bringing the radius on one side:
\[radius^2 = \frac{Area}{\pi}\]
Taking the square root of both sides:
\[radius = \sqrt{ \frac{Area}{\pi}}\]

Answer 5

so the radius is 6.10?

Answer 6

Yes, just round that value to the nearest inch.

Answer 7

Now, for C.... how do I find the area of one cookie wedge if its central angle measures 15 degrees?

Answer 8

Finally, part C.

Using the following equation to get the area inside a central angle of a circle:
\[Area = \frac{Angle}{360} * \pi * radius^2\]
Use 15 degrees for the angle and the value you calculated in part B for the radius.

Answer 9

Notice that this equation is very similar to that for calculating the area of a circle.

Answer 10

Is the answer 4.17?

Answer 11

**4.71

Answer 12

That looks right to me, just make sure to round it to the nearest inch.

Answer 13

thanks could u help me with this problem?

Answer 14

Sure. Since this triangle is a right triangle, we can use the Pythagorean Theorem:
\[a^2 + b^2 = c^2\]
Which for our purposes can be rewritten:
\[side^2 + side^2 = hypotenuse^2\]
Adding like terms:
\[2*side^2 = hypotenuse^2\]
So now we can plug in the length of the hypotenuse and calculate the length of the sides.

Answer 15

Divide both sides by 2:
\[side^2 = \frac{hypotenuse^2}{2}\]
Taking the square of both sides:
\[side = \sqrt{\frac{hypotenuse^2}{2}}\]

Answer 16

Can you please give me the answer to a? that way...I can figure out b because I don't understand.

Answer 17

The problem states that the hypotenuse of the triangle is 30 cm. Plugging this into the equation above gives:
\[side = \sqrt{\frac{(30cm)^2}{2}}\]
Squaring the hypotenuse:
\[side = \sqrt{\frac{900cm^2}{2}}\]
Dividing by 2:
\[side = \sqrt{450cm^2}\]
Separating the units:
\[side = \sqrt{450} * \sqrt{cm^2}\]
Simplifying:
\[side = \sqrt{450} cm^2\]
So the answer is the square root of 450 in cm, rounded to the nearest tenth of a centimeter.

Answer 18

Ah! Thanks so much! Greatly Appreciated!
IF you want to help, here is my next question.

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The booster club at the highschool sells blankets at the football games with paw prints. Estimate the area the paw print covers.

Answer 19

You're welcome! Glad I could help. I'm up for another one.

Answer 20

Thanks so much!

Answer 21

First, notice that the toes of the paw prints take up a little more than a square foot each. That gives us approximately:
\[1ft^2 * 4 = 4ft^2\]
The heel of the paw print takes up a whole square foot, plus two half square foot sections and quite a bit left over. This gives us at least an additional:
\[1ft^2 + 2*\frac{1}{2}ft^2 = 1ft^2 + 1ft^2 = 2ft^2\]
The amounts left over might be enough to fill another square foot, but I'm not certain. So, my estimate for the amount of area the paw prints cover is:
\[4ft^2 + 2ft^2 (+ 1ft^2)\]
With the part in parenthesis being optional.

Answer 22

Are you up for more homework problems or are you sick of me yet!? :)

Answer 23

That depends on whether you're learning anything, lol!

Answer 24

I am! A ton! Thank you so much!! Could you check my work on these problems? Geometry is not my thing.

Answer 25

How did you get the parameter of C?

Answer 26

1.a. and 2.a. look correct.

Answer 27

For c, I got 72.75 by