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Math Help - Finding the Surface Area of a Cone?

  1. #1
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    Finding the Surface Area of a Cone?

    I am reviewing for the 11th grade state assessment tests which are coming up soon. The formula I am given for finding the surface area of a cone is:

    SA = πr + πr √r + h

    The information I am given in the example problem is: r = 3 cm, h = 4 cm.

    ----------
    I am not here to ask for the answer - I simply wonder what to do next. My work so far looks like this:

    SA = πr + πr √r + h
    SA = π(3) + π(3) √(3) + (4)
    SA = 37.699 √25

    The correct answer in this question is given: 75.36 sq cm. Did I do my order of operations wrong (for what I have shown), and, how do you find the final answer?

    Any help is appreciated, thank you.
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  2. #2
    A riddle wrapped in an enigma
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    Quote Originally Posted by AlderDragon View Post
    I am reviewing for the 11th grade state assessment tests which are coming up soon. The formula I am given for finding the surface area of a cone is:

    SA = πr + πr √r + h

    The information I am given in the example problem is: r = 3 cm, h = 4 cm.

    ----------
    I am not here to ask for the answer - I simply wonder what to do next. My work so far looks like this:

    SA = πr + πr √r + h
    SA = π(3) + π(3) √(3) + (4)
    SA = 37.699 √25

    The correct answer in this question is given: 75.36 sq cm. Did I do my order of operations wrong (for what I have shown), and, how do you find the final answer?

    Any help is appreciated, thank you.
    Hi AlderDragon,

    S.A.=\pi r^2+\pi r \sqrt{r^2+h^2}

    S.A.=\pi \cdot 3^2 + 3\pi \sqrt{3^2+4^2}

    S.A.=\pi \cdot 9 + 3\pi \sqrt{25}

    S.A.=9 \pi + 15 \pi

    S.A. \approx 75.4 \,cm^2
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