Question

2. The area of the base of the cone is 64π cm2 and the altitude is 6 cm. Calculate the cone: (a) the length of the constituent;(b) the area of the lateral area of the cone; c) the volume.

Answer 1

Answer: We have to calculate the (i) volume and (ii) the surface area of the cone:

$\begin{gathered} A=\pi r^2+\pi rl\rightarrow(1) \\ \\ V=\pi r^2\frac{h}{3}\rightarrow(2) \end{gathered}$

The formula (1) is for the lateral surface of the cone and the formula (2) is for the volume of the cone, the unknowns are determined as follows:

$\begin{gathered} r=\sqrt{\frac{64\pi}{\pi}}=8cm \\ \\ r=8cm \\ \\ l=\sqrt{r^2+h^2}=\sqrt{(8cm)^2+(6cm)^2} \\ \\ l=\sqrt{100}=10 \\ \\ l=10 \end{gathered}$

Therefore the volume and the lateral surface area is calculated as follows:

$\begin{gathered} \begin{equation*} A=\pi r^2+\pi rl \end{equation*} \\ \\ A=\pi(8)^2+\pi(8)(10) \\ \\ A=144\pi cm^2\Rightarrow(x) \\ \\ \begin{equation*} V=\pi r^2\frac{h}{3} \end{equation*} \\ \\ V=\pi(8cm)^2\frac{6cm}{3} \\ \\ V=128\pi cm^3\Rightarrow(y) \end{gathered}$

Therefore x and y are the answers.