Question

The radius and height of a cone are in the ratio 4: 3. The area of the base is 154 cm². Find the total suraface area of the cone.

• A. $246.5c{m}^2$
• B. $346.5c{m}^2$
• C. $446.5c{m}^2$
• D. $336.5c{m}^2$

Answer 1

The correct option is B $346.5c{m}^2$

Given,
$\Rightarrow \frac{r}{h}$ = $\frac{4}{3}$

Base area
$\Rightarrow \pi$$r^2=154$
$\Rightarrow \frac{22}{7}$$\times$$r^2=154$
$\Rightarrow r=7cm$

So,
$h=\frac{3}{4}\times 7=\frac{21}{4}cm$

We know that,
$l=\sqrt{(h^2+r^2)}$
$\Rightarrow l=\sqrt{\left(\right(\frac{21}{4}{)}^2+7^2)}$
$\Rightarrow l=\frac{35}{4}$

$\therefore$ Total surface area of cone
$=\pi$$rl$ + $\pi r^2$
$=\frac{22}{7}\times \left(7\right)\times \frac{35}{4}$ + $\frac{22}{7}\times 7^2$
$=192.5c{m}^2$ + $154c{m}^2$
$=346.5c{m}^2$