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Math Help - Isosceles pizza...

  1. #1
    Newbie PrincessKiara's Avatar
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    Question Isosceles pizza...

    Hello! I was looking for help on the 'Net and happened to stumble on this site. It looks good so I just decided to drop in!
    I have a math test and I need to know if my answer is correct. It's a multiple-choice test, but the answer I'm getting isn't matching any of the options. I'm pretty sure I did it correctly, but it's not showing up. I am
    not asking for the answer; I simply need to know if I'm right and the test is messed up or if not how I should do it to get it right. Here's the problem:

    If a slice of medium pizza 30 cm in diameter is divided into five equal parts, cutting it along radii from the center, what is the surface area of each slice of pizza?

    The options are:

    a) 565.48 cm2 b) 708.86 cm2 c) 141.39 cm2 d) 18.8 cm2
    Here's how I solved it, or thought I did, LOL!

    (30)(3.1416)= 94.248 94.248/5=18.8496 18.8496/2=9.4248

    Now the isosceles triangle has become a right triangle with a base of 9.4248 cm and a hypotenuse of 15 cm. So I applied the Pythagorean theorem to find the height.

    152-9.42482=h2 152=225 9.42482=88.82685504 225-88.82685504=136.17314496


    The square root of 136.17314496 is 11.66932495734008, so b=9.4248 cm and h=11.66932495734008 cm. I did all that math both by hand and on a calculator, so I know it's right!

    Now I'll apply the formula for the area:

    (b)(h)/2=(18.8496)(11.66932495734008)/2=219.9621077158775/2=109.9810538579388

    So according to my calculations, the pizza slices' surface areas should be equal to 109.9810538579388 cm2 per slice, yet that's not among the listed options. You see my dilemma I realize this may be elementary, my dear Watson, but I guess I just haven't grasped it yet Any help will be greatly appreciated!

    Thank you!
    ~PK.
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  2. #2
    MHF Contributor
    skeeter's Avatar
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    Re: Isosceles pizza...

    a slice of pizza is the sector of a circle, not an isosceles triangle ... just find the circular pizza's area ( \pi r^2 , right?) and divide the result by 5.
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  3. #3
    Newbie PrincessKiara's Avatar
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    Re: Isosceles pizza...

    Thank you! I feel so dumb now....
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  4. #4
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    Re: Isosceles pizza...

    The pieces of pizza do not form perfect triangles as the ends are rounded. Your right triangle will only approximate the answer. Wouldn't it be easier to find the area of the whole pizza and divide it by the number of pieces since they are all the same?
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