Question

determine the volume and the surface area of the three - dimensional figure. use the π key on your calculator.

a) the volume is 29.32 cm³ (simplify your answer. type an integer or a decimal rounded to the nearest hundredth as needed.)

b) the surface area is cm² (simplify your answer. type an integer or a decimal rounded to the nearest hundredth as needed.)

Explanation:

Step1: Find the slant height \( l \)

Use the Pythagorean theorem \( l=\sqrt{r^{2}+h^{2}} \). Given \( r = 2\mathrm{cm}\) and \( h=7\mathrm{cm}\), then \( l=\sqrt{2^{2}+7^{2}}=\sqrt{4 + 49}=\sqrt{53}\mathrm{cm}\)

Step2: Calculate the surface area of the cone

The surface area formula of a cone \( S=\pi r(r + l)\). Substitute \( r = 2\) and \( l=\sqrt{53}\) into the formula:

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Using the \( \pi\) key on the calculator: \( S=2\times3.1416\times9.2801\approx58.30\mathrm{cm}^{2}\)

Answer:

\(58.30\)