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The area of base of a cone is $616 c m^{2}$ and its height is $48 cm$ . The total surface area of the cone is

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2816 c m^{2}

2861 c m^{2}

2618 c m^{2}

2681 c m^{2}

answer is A.

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Detailed Solution

Given: Base area of cone

= 616 c m^{2}

Height of cone

= 48 cm

Base area of cone = Area of circle = π r^{2}

\Rightarrow π r^{2} = 616 c m^{2}

r^{2} = 616 \times \frac{7}{22}

r = \sqrt{28 \times 7} = 14 cm

Slant height = \sqrt{r^{2} + h^{2}}

l = \sqrt{{(14)}^{2} + {(48)}^{2}} = \sqrt{2500} = 50 cm

Total surface area of cone

= πrl + π r^{2}

\Rightarrow πr (l + r)

\Rightarrow \frac{22}{7} \times 14 (50 + 14)

\Rightarrow 22 \times 2 \times 64

\Rightarrow 2618 c m^{2}

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