Question

The diameter of a cone is 14 cm and slant height is 25 cm . Find the volume of the cone

Answer 1

Answer:

d = 14 cm

r = 7 cm

slant height (l) = 25 cm

(l)² = (h)²+(r)²

(h)^2 = (l)^2 - (r)^2

(h)^2 = (25)²-(7)²

h=root 576 = 24 cm

vertical height = 24 cm [ This is your answer ]

hope it helps

tq..//

Step-by-step explanation:

Answer 2

Given :

• Diameter of cone = 14 cm
• Slant height = 25 cm

To Find :

• The volume of the cone

Solution :

The relation between diameter and radius is ,

$\\ : \implies \sf \: d = 2r$

We have ,

• diameter (d) = 14 cm

$\\ : \implies \sf \: 14 \: cm = 2r$

$\\ : \implies \sf \: r = \frac{14 \: cm}{2}$

$\\ : \implies \boxed{\red{\mathfrak{ \: r = 7 \: cm }}}\:$

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Now , The relation between Slant height (l) , radius (r) and height (h) of a cone is given by ;

$\\ \star \: {\boxed{\sf{\purple{ {l}^{2} = {r}^{2} + {h}^{2} }}}}$

We have ,

• Slant height (l) = 25 cm
• Radius (r) = 7 cm

Substituting the values ,

$\\ : \implies \sf \: {(25\:cm)}^{2} = {(7\:cm)}^{2} + {h}^{2}$

$\\ :\implies \sf \: 625\:cm^2 = 49 \:cm^2+ {h}^{2}$

$\\ : \implies \sf \: 625\:cm^2 - 49\:cm^2 = {h}^{2}$

$\\ : \implies \sf \: 576\:cm^2 = {h}^{2}$

$\\ : \implies \sf \: h = \sqrt{576\:cm^2}$

$\\ : \implies{\boxed{\mathfrak{\red{h = 24 \: cm}}}}$

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Volume of a cone is given by ,

$\\ \star \: {\boxed{\purple{\sf{v = \frac{1}{3}\pi {r}^{2} h }}}}$

We have ,

• r = 7 cm
• h = 24 cm

Substituting the values ,

$\\ : \implies \sf \:v = \frac{1}{3} \times \frac{22}{7} \times {(7\:cm)}^{2} \times 25\:cm$

$\\ : \implies \sf \: v = \frac{1}{3} \times 22 \times 7\:cm^2 \times 25\:cm$

$\\ : \implies \sf \: v = \frac{3850 \: cm {}^{3} }{3}$

$\\ : \implies{\boxed{\pink{\sf{v = 1283.33 \: \: {cm}^{3} }}}} \: \bigstar$

$\\ \therefore \underline{ \sf{Hence\:, The\:Volume\:of\:the\:cone\:is\: \bold{1283.33\:cm^3}}}$