Question

determine the volume and the surface area of the three - dimensional figure. use the (pi) key on your calculator.
a) the volume is (815.75 mathrm{~cm}^{3}) (simplify your answer. type an integer or a decimal rounded to the nearest hundredth as needed.)
b) the surface area is (square mathrm{cm}^{2}) (simplify your answer. type an integer or a decimal rounded to the nearest hundredth as needed.)

Explanation:

Step1: Calculate the slant height \( l \)

The formula for the slant height of a cone is \( l=\sqrt{r^{2}+h^{2}} \). Given \( r = 7\mathrm{cm} \) and \( h=12\mathrm{cm} \), then \( l=\sqrt{7^{2}+12^{2}}=\sqrt{49 + 144}=\sqrt{193}\approx13.89\mathrm{cm} \).

Step2: Calculate the surface area \( S \)

The formula for the surface area of a cone is \( S=\pi r(r + l) \). Substitute \( r = 7\) and \( l\approx13.89 \) into the formula: \( S=\pi\times7\times(7 + 13.89)=7\pi\times20.89\approx7\times3.14\times20.89=461.58\mathrm{cm}^{2} \)

Answer:

\( 461.58 \)