The radius and height of a cone are in the ratio 4: 3. The area of the base is 154cm 2 . The area of the curved surface in c m 2 __ Options:

Answer: Option A : r h = 4 3 Base area = π r 2 = 154 ⇒ r = 7 c m so h = 3 4 × 7 = 21 4 ⇒ l = √ ( h 2 + r 2 ) = 35 4 ⇒ So, curved surface area = π r l ⇒ 22 7 × ( 7 ) × 35 4 = 192.5 c m 2

The radius and height of a cone are in the ratio 4: 3. The area of the base is

Question

The radius and height of a cone are in the ratio 4: 3. The area of the base is 154cm². The area of the curved surface in $c m^{2}$

Options:

Answer: Option A
:

$\frac{r}{h}$ = $\frac{4}{3}$

Base area = $π$ $r^{2} = 154$

$\Rightarrow r = 7 c m$ so $h = \frac{3}{4} \times 7 = \frac{21}{4}$
$\Rightarrow l = \sqrt{(h^{2} + r^{2})} = \frac{35}{4}$

$\Rightarrow$ So, curved surface area = $π$ $r l$

$\Rightarrow$ $\frac{22}{7} \times (7) \times \frac{35}{4} = 192.5 c m^{2}$

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