Question

The volume of a right circular cone is 1232 cm3 and its vertical height is 24 cm. Its curved surface area is

Answer 1

Solution :

Find Radius of the right circular Cone

We have Given ,

Volume = $1232 cm^3$

Volume of Cone = $\frac{1}{3} \pi r^2h$

⇒ = $\frac{1}{3} \pi r^2h$ = $1232 cm^3$

⇒ $\frac{1}{3} * \frac{22}{7} * r^2 * 24 = 1232$

⇒ $r^2 = \frac{1232 * 3* 7}{22 * 24} = 49$

⇒ $r = \sqrt{49}$

⇒ r = 7 cm

Find Slant height of the right Circular Cone

$l = \sqrt{r^2 + h^2}$

⇒ $\sqrt{7^2 + 24^2}$

⇒ $\sqrt{625}$

⇒ 25 cm

Find the Curved Surface area of the Cone

Curved Surface area = $\pi rl$

⇒ $\frac{22}{7} * 7 * 25$

⇒ $550 cm^2$

Answer :

The Surface area is 550 cm^2

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Answer 2

$\bold \red{here \: is \: your \: answer}$
Volume is given => 1232

then,,,,,
$\frac{1}{3} \ {\pi}^{2} h = 1232$

$\frac{1}{3} \times \frac{22}{7} \times {r}^{2} \times 24 = 1232$

now,,,,
${r}^{2} = \frac{1232 \times 3 \times 7}{22 \times 24} = 49$


Therefore,,,
$r = \sqrt{49} = 7 \: cm$

therefore slant height =
$\sqrt{ {r}^{2} + {h}^{2} } = \sqrt{7 + {24}^{2} } = \sqrt{625 } = 25 \: cm$


then,,, curved surface of cone =
$\pi \: r \: l$

=>
$\frac{22}{7} \times 7 \times 25 = 550 {cm}^{2}$



thanks for asking this question