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The vertical angle of a right circular cone is π/2 and the slant height is √2r cm. What is the volume of the cone in cubic cm?
- a)πr3
- b)9π3
- c)πr3/3
- d)3πr3
Correct answer is option 'C'. Can you explain this answer?
Verified Answer
The vertical angle of a right circular cone is π/2 and the slant he...
Semi - vertical angle, α = ½ × π/2 = π/4 = 45°
Slant height, l × sinα = radius
⇒ √2r × sin 45° = √2r × 1/√2 = r = radius
⇒ Height = rtanα = rtan45° = r
∴ Volume of the cone = 1/3πr2H = πr3/3
Slant height, l × sinα = radius
⇒ √2r × sin 45° = √2r × 1/√2 = r = radius
⇒ Height = rtanα = rtan45° = r
∴ Volume of the cone = 1/3πr2H = πr3/3
Most Upvoted Answer
The vertical angle of a right circular cone is π/2 and the slant he...
Semi - vertical angle, α = ½ × π/2 = π/4 = 45°
Slant height, l × sinα = radius
⇒ √2r × sin 45° = √2r × 1/√2 = r = radius
⇒ Height = rtanα = rtan45° = r
∴ Volume of the cone = 1/3πr2H = πr3/3
Slant height, l × sinα = radius
⇒ √2r × sin 45° = √2r × 1/√2 = r = radius
⇒ Height = rtanα = rtan45° = r
∴ Volume of the cone = 1/3πr2H = πr3/3
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Community Answer
The vertical angle of a right circular cone is π/2 and the slant he...
Given data:
Vertical angle of the cone = π/2
Slant height = √2r
Formula for volume of cone:
Volume = (1/3)πr^2h
Calculation:
- The vertical angle of the cone being π/2 means that the cone is a right circular cone.
- The slant height of the cone is given as √2r.
- When the vertical angle of the cone is π/2, the slant height is the hypotenuse of a right triangle formed by the height, radius, and slant height of the cone.
- Using Pythagoras theorem, we can find the height of the cone as h = r.
- Substituting the values of radius (r) and height (h) into the formula for volume of cone, we get:
Volume = (1/3)πr^2h
Volume = (1/3)πr^2r
Volume = (1/3)πr^3
Therefore, the volume of the cone is given by option 'c': πr^3/3.
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