Question

What is the total surface area of a right circular cone of height $14cm$ and a circular base of radius $7cm$?

• A. $462{cm}^2$
• B. $344.35{cm}^2$
• C. $498.35{cm}^2$
• D. None of these

Answer 1

Answer: (C)

Given that,

Height of cone $h=14cm$ ...(i)

Radius of base $r=7cm$ ...(ii).

We know that,

Total surface area, $A=\pi r(r+l)=\pi r(r+\sqrt{h^2+r^2})$....(Since, $l^2=r^2+h^2$).

Substituting the value from (i) & (ii),

$A=\pi \left(7\right)(7+\sqrt{(14{)}^2+7^2})$

$=7\pi (7+\sqrt{245})$

$=7\pi (7+15.65)$

$=7\times 3.14(7+15.65)$

$=498.35c{m}^2$

$\therefore A=498.35c{m}^2$.

Hence, option $C$ is correct.