Question

multiple choice (single... as shown in the figure, it is known that (ab = 6mathrm{cm}) and (ob = 3mathrm{cm}). find the surface area of this cone.
a (21pimathrm{cm}^2)
b (27pimathrm{cm}^2)
c (36pimathrm{cm}^2)
d (45pimathrm{cm}^2)

Explanation:

Step1: Identify slant - height and radius

The slant - height \(l\) of the cone is \(AB = 6\mathrm{cm}\), and the radius \(r\) of the base is \(OB=3\mathrm{cm}\).

Step2: Recall the formula for the surface area of a cone

The surface area of a cone \(S=\pi rl+\pi r^{2}\).

Step3: Substitute the values into the formula

Substitute \(r = 3\mathrm{cm}\) and \(l = 6\mathrm{cm}\) into the formula:
\[

$$\begin{align*} S&=\pi\times3\times6+\pi\times3^{2}\\ &=18\pi + 9\pi\\ &=27\pi\mathrm{cm}^{2} \end{align*}$$

\]

Answer:

B. \(27\pi\mathrm{cm}^{2}\)