a metallic sheet form of a sector of a circle of radius 21cm has central angle of 216°.The sector is made into a cone by bringing the bounding radii together. Find the volume of cone formed
Answers
The volume of the cone-formed is 2794.176 cm³.
Step-by-step explanation:
It is given that,
The radius of the sector of a circle formed from a metal sheet, r = 21 cm
The central angle, θ = 216°
Step 1:
Now, it is rolled up to form a cone.
So, we get
The circumference of the base of the cone is,
= Length of the arc of the sector
= (θ/360) * 2πr
= (216/360) * 2π * 21
= (3/5) * 2 * (22/7) * 21
= 79.2 cm
Step 2:
We know that the circumference of circle = 2πr
So, we can write
The circumference of the base of cone = 2πr
⇒ 79.2 = 2πr
⇒ 79.2 = 2 * (22/7) * r
⇒ r = [79.2 * 7]/[2 * 22]
⇒ r = 12.6 cm ← radius of base of cone
Also,
The slant height of the cone (l) = radius of the sector = 21 cm
We know that slant height
l = √(h² + r²)
⇒ l² = (h² + r² )
⇒ 21² = h² + 12.6²
⇒ h = √[441 – 158.76]
=> h = √[282.24]
=> h = 16.8 cm ← height of the cone
Thus, substituting the value of r = 12.6 cm and h = 16.8 cm, we get
The volume of the cone is given by,
= 1/3 * π * r² * h
= (1/3) * (22/7) * 12.6² * 16.8
= (1/3) * (22/7) * 158.76 * 16.8
= 2794.17 cm³
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Also View:
A sector of a circle of radius 6 cm has an angle of 120°. it is rolled up so that the two bounding radii are joined together to form a cone.
Find
1) the total surface area of cone
2) the volume of the cone
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From a circle of radius 15 cm a sector with angle 216 degree is cut out and its bounding radii are bent so as to form a cone find the volume?
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A sector of circle of radius 12cm has the angle 120 degree. it is rolled up so that the two bounding radii are formed together to form a cone. find the volume of cone and total surface area of cone?
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Answer:
We know length of the arc l = x°/360° = 2πr
∴ Arc AB = 216°/ 360° × 2π × 21
= 216°/360° × 2 × π × 21
- When the radii OA and OB brought together we get a cone whose slant height is OA and perimeter of the base is arc AB.
Perimeter of the base of the cone = arc AB
2πr1 = 216/369 × 2π × 21
r1 = 216/360 × 21
r1 = 12.6cm
Base radius of the cone r = 12.6cm
Slant height of the cone l = 21cn
∴ Height of the cone h = √l^2 - r^2
= √21^2 - (12.6) ^2
= √441 - 158.76
h = √282.24 = 16.8cm
Volume of the cone = 1/3 πr1^2 h cu.units
= 1/3 × 22/7 × 12.6 × 12.6 × 16.8
= 58677.696 / 21
VOLUME OF THE CONE =
2794.18cm^3
Step-by-step explanation:
@GENIUS