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    Find the total surface area of a cone of slant height '2l' and radius 'r/2'.
    Question

    Find the total surface area of a cone of slant height '2l' and radius 'r/2'.

    A.

    πr (l + r)

    B.

    2πTr(l + r)

    C.

    2πrl

    D.

    (πrl+πr24)( \pi r l + \frac{\pi r^2}{4})​​

    Correct option is D

    Given:

    The slant height ls=2l l_s = 2l  and radius r=r2 r = \frac{r}{2}

    Formula Used :

    A=πrl+πr2A = \pi r l + \pi r^2​​

    Solution:

    Substitute the values into the formula for total surface area:

    A=π(r2)(2l)+π(r2)2A = \pi \left( \frac{r}{2} \right) (2l) + \pi \left( \frac{r}{2} \right)^2​​

    Simplifying the expression:

    A=π(r2)(2l)+πr24A = \pi \left( \frac{r}{2} \right) (2l) + \pi \frac{r^2}{4}​​

    A=πrl+πr24A = \pi r l + \frac{\pi r^2}{4}​​

    Thus, the total surface area of the cone is (πrl+πr24)( \pi r l + \frac{\pi r^2}{4})​​

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