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Calculate the total surface area of a frustum cone:

D = 1 cm, d = 0.1 cm, h = 5 cm.

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18.298

{cm}^{2}

17.298

{cm}^{2}

16.298

{cm}^{2}

11.159

{cm}^{2}

answer is D.

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Detailed Solution

Given that,
D = 1 cm, d = 0.1 cm, h = 5 cm.
Diameter = radius

\times 2

R = 0.5 cm, r = 0.05 cm
Total surface area of frustum =

π (R + r) \sqrt{(R - r)^{2} + h^{2}} + π R^{2} + π r^{2}

\Rightarrow

3.14 (0.5 + 0.05) \sqrt{(0.5 - 0.05)^{2} + 5^{2}} + π {0.5}^{2} + π {0.05}^{2}

\Rightarrow

3.14 \times (0.550) \times 5.020 + 0.25 \times 3.14 + 0.0025 \times 3.14

\Rightarrow

3.14 [2.761 + 0.785 + 0.00785]

\Rightarrow

11.159 {cm}^{2}

Therefore, total surface area =

11.159 {cm}^{2}

.
Hence, the correct option is 4.

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