Question

If the height and slant height of a cone are 3 cm and 5 cm respectively. Then volume is : 
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Answer 1

Answer:

$50.24cm^{3}$

Step-by-step explanation:

Given:

h= 3cm

l= 5cm

$r$ = $\sqrt{l^{2}-h^2 }$ = $\sqrt{5^2 - 3^2}$ = $\sqrt{25 - 9}$ = $\sqrt{16} = 4cm$

∴ The volume of a cone = $\frac{1}{3}$ π $r^{2} h$

= $\frac{1}{3} * 3.14 * 4^2 * 3$ = $\frac{150.72}{3} = 50.24 cm^3.$

Answer 2

Step-by-step explanation:

Diagram:- Refer the attachment

Given:-

• The height of the cone = 3cm

• The slant height of the cone = 5cm

To Find:-

• The volume of the cone.

Solution:-

Height (h) = 3cm

Slant height (l) = 5cm

Let the radius of the cone be r

As, we know that:-

$\sf \implies {l}^{2} = {r}^{2} + {h}^{2}$

$\sf \implies {r}^{2} = {l}^{2} - {h}^{2}$

$\sf \implies {r}^{2} = {5}^{2} - {3}^{2}$

$\sf \implies {r}^{2} = 25 - 9$

$\sf \implies {r}^{2} = 16$

$\sf \implies r = \sqrt{16} = 4cm$

$\sf \therefore Radius \: of \: the \: cone = 4cm$

$\sf Volume \: of \: the \: cone = \dfrac{1}{3}\pi r^2 h$

$\sf \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = \dfrac{1}{3} \times \dfrac{22}{7} \times {4}^{2} \times 3$

$\sf \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = \dfrac{22}{7} \times 16$

$\sf \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = \dfrac{342}{7}$

$\sf \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = 50.285$

$\underline{\boxed{\sf \therefore Volume \: of \: the\: cone = 50.285cm^3}}$