A right circular cylinder whose diameter is equal to its height is inscribed in a right circular cone of
base diameter 16 cm and height 3 times the base diameter. What is the volume of the solid inside the
cone but outside the cylinder?
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Step-by-step explanation:
A right circular cylinder whose diameter is equal to its height is inscribed in a right circular cone of base diameter 16 cm and height 3 times the base diameter. What is the volume of the solid inside the cone but outside the cylinder?
- Now inside a cone a cylinder is placed inside it. The base diameter is 16 cm
- So radius r = d/2
- = 16/2
- = 8 cm
- It is given the height is 3 times the base diameter.
- h = 16 x 3 = 48 cm
- the volume in a cone should be found and not in cylinder.
- So subtracting volume of cone – volume of cylinder
- So volume of cone
- V = 1/3 π r^2 h
- = 1/3 π (8)^2 x 48
- = 1024 cm^3
- Now d = h
- So 2r = h (since diameter = 2 radius)
- Assume a drawing a diagram and we get
- h/8 – r = 48/ 8
- Substituting h = 2r we get
- 2r / 8 – r = 6
- 2r = 6(8 – r)
- 2r = 48 – 6r
- 8r = 48
- Or r = 6 cm
- Now we have
- h = 2r
- h = 2 x 6
- Or h = 12 cm
- Also we have volume of cylinder is π r^2h
- = π (6)^2 x 12
- = π x 432 cm^3
- Now according to question volume of cone – volume of cylinder will be
- = 1024 π – 432 π
- = 592 π
- = 1858.88
Reference link will be
https://brainly.in/question/15974924
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