A metallic sheet in the form of a sector of a circle of radius 2lcm has central angle or 216 degree.
The sector is made into a cone by bringing the bounding radii together. Find the volume of
the cone formed.
Answers
Answer:
Solution
A metallic sheet is form of a sector of a circle of radius 21 cm and has central angle of 216°
→ The cone formed by it would have
l (slant height) = 21 cm
And, part of circumference of the sector would be the circumference of base
Part of circumference formed by sector = 2πr × ∅/360
Taking π as 22/7,
→ 2 × 22/7 × 21 × 216/360
→ 79.2 cm
This would act as the circumference of the base of cone
Let the base radius of cone be R
→ 2πR = 79.2 cm
→ R = 79.2 × 7/22 × 1/2
→ R = 12.6 cm
Now, we know that
l² = h² + R²
So, we will find height of the cone from here
→ 21² = h² + (12.6)²
→ h² = 441 - 158.76
→ h² = 282.24
→ h = 16.8 cm
Now we know that volume of cone = 1/3 × πr²h
→ 1/3 × 22/7 × 12.6 × 12.6 × 16.8
→ 2794.176 cm³
Answer:
2794.176 cm³
Step-by-step explanation:
A metallic sheet is form of a sector of a circle of radius 21 cm and has central angle of 216°
→ The cone formed by it would have
l (slant height) = 21 cm
And, part of circumference of the sector would be the circumference of base
Part of circumference formed by sector = 2πr × ∅/360
Taking π as 22/7,
→ 2 × 22/7 × 21 × 216/360
→ 79.2 cm
This would act as the circumference of the base of cone
Let the base radius of cone be R
→ 2πR = 79.2 cm
→ R = 79.2 × 7/22 × 1/2
→ R = 12.6 cm
Now, we know that
l² = h² + R²
So, we will find height of the cone from here
→ 21² = h² + (12.6)²
→ h² = 441 - 158.76
→ h² = 282.24
→ h = 16.8 cm
Now we know that volume of cone = 1/3 × πr²h
→ 1/3 × 22/7 × 12.6 × 12.6 × 16.8
→ 2794.176 cm³
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