Question

16. Find the volume and surface area of the cone. Round to the nearest hundredth. (4pts)10 cmI20 cmVolume =Surface Area =

Answer 1

Volume = 12560 cm^3

Surface Area = 2660.2 cm^2

Explanation:

To calculate the volume of a cone, the following formula must be applied

`\begin{gathered} V=A_b\cdot h \\ A_b=\pi\cdot r^2 \end{gathered}`

Replacing and solving the volume:

`\begin{gathered} V=3.14\cdot20^2\cdot10 \\ V=12560cm^3 \end{gathered}`

To calculate the surface area of a cone, the following formula must be applied

`\begin{gathered} SA=\pi\cdot r\cdot s+\pi\cdot r^2 \\ s^2=r^2+h^2\rightarrow s=\sqrt[]{r^2+h^2} \end{gathered}`

Replacing and solving the surface area:

`\begin{gathered} SA=3.14\cdot20\cdot\sqrt[]{10^2+20^2}+3.14\cdot20^2 \\ SA=3.14\cdot20\cdot22.36+3.14\cdot20^2 \\ SA=1404.2+1256 \\ SA=2660.2cm^2 \end{gathered}`