Question

Consider a cone whose base area is equal to $154{\mathrm{cm}}^2$ and the slant height is $9\mathrm{cm}$ then

• A. Curved surface area $=198{\mathrm{cm}}^2$
• B. Total surface area $=300{\mathrm{cm}}^2$
• C. Total surface are $=352{\mathrm{cm}}^2$
• D. Height of the cone $=4\sqrt{2}\mathrm{cm}$

Answer 1

Answer: (A), (C), (D)

$\therefore \pi r^2=154\Rightarrow \frac{22}{7}\times r^2=154$
$\therefore r=7\mathrm{cm}$
$\text{ Curved surface area }=\pi rl$
$=\frac{22}{7}\times 7\times 9$
$=198{\mathrm{cm}}^2$
$\text{ Total surface are }=\pi rl+\pi r^2$
$=198+154$
$=352{\mathrm{cm}}^2$
As, $h^2+r^2=l^2$
[Where $h\to$ height of the cone]
$\therefore h^2=l^2-r^2$
$\therefore h=\sqrt{9^2-7^2}$
$\therefore h=\sqrt{32}$
$\therefore h=4\sqrt{2}\mathrm{cm}$