Question

Calculate the surface area of a cone whose radius is $\frac{1}{3}$ cm and slant height is $12$ cm.

• A. $3\pi$ $c{m}^2$
• B. $\frac{37\pi }{9}$ ${cm}^2$
• C. $\frac{37\pi }{8}$ ${cm}^2$
• D. $\frac{5\pi }{9}$ ${cm}^2$

Answer 1

Answer: (B)

$\frac{37\pi }{9}$ ${cm}^2$

Surface area of cone is $A=\pi r(r+l)$.

Here, radius is $r=\frac{1}{3}$ cm and slant height is $l=12$ cm.

Thus,

$A=\pi r(r+l)=\pi \times \frac{1}{3}(\frac{1}{3}+12)=\frac{1}{3}\pi \times \frac{37}{3}=\frac{37\pi }{9}$ cm${}^2$.

Hence, the surface area of the cone is $\frac{37\pi }{9}$ cm${}^2$.

Therefore, option $B$ is correct.