Math, asked by sahasra529123, 2 months ago

5. From a circle of radius 15 cm., a sector with angle 216° is cut out and its bounding radii are bent so as to form a cone. Find its volume.

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Answers

Answered by BrainlyRuhi
9

Answer:

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Here,

Radius of the circle, R = 15 cm

When the sector is cut and its bounding radii is bent to form a cone,

Slant height of the cone, l = R = 15 cm

Let r and h be the radius and height of the cone, respectively.

Again, we know that in a circle of radius R, an arc of length X subtends an angle of θ radians, then

x=Rθ

Here, the arc length will be equal to the perimeter of the base circle of the cone.

x=2πr

2πr=Rθ

 \frac{r}{R}  =  \frac{θ}{2πr}

⇒ \frac{r}{15}  =  \frac{216}{360}

⇒r = 9cm

Now, height of the cone can be calculated as,

➣ h² = l² - r²

➣ h² = (15)² −( 9)²

➣ h² = 225 − 81

➣ h =  \sqrt{144} = 12 cm

Therefore,

Volume of the cone, V = 3/1 πr² h= 3/1 × 22/7 ×81×12 = 1018.28 cm³

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  • Hence, this is the required result.

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