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The curved surface area of a frustum cone is 2.34 ${cm}^{2}$ . The larger circle area is 12.5 ${cm}^{2}$ . The total surface area is 25.8 ${c m}^{2}$ . Find the smaller circle area of a cone.

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12.96

{cm}^{2}

11.96

{cm}^{2}

10.96

{cm}^{2}

9.96

{cm}^{2}

answer is C.

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Detailed Solution

Given curved surface area of a frustum cone 2.34

{cm}^{2}

, larger circle area 12.5

{cm}^{2}

and total surface area 25.8

{cm}^{2}

.
Total surface area = curved surface area + Area of smaller circle + larger circle area

\Rightarrow 25.8 = 2.34 +

Area of smaller circle + 12.5

\Rightarrow 25.8 - 2.34 - 12.5 =

Area of smaller circle

\Rightarrow

Area of smaller circle = 10.96

{cm}^{2}

.
Therefore, area of smaller circle of a frustum cone = 10.96

{cm}^{2}

.
Hence, the correct option is 3.

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