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