Rachel and engineering student was asked to make a model shaped like a cylinder with two cones attached to at its two ends by using a thin aluminium sheet the diameter of the model is 3 cm its length is 12 CM if each one has a height of 2 cm find the volume of the air conditioner in the model that Richard made assume that the outer and the inner dimensions of the model to be nearly the same
Answers
Answer:
66cm3.
Step-by-step explanation:
volume of air in the solid = volume of the cylinder + 2(volume of the cone).
= πr2h + 2 ( 1/3 π r2h ) d = 3 cm, r = 3/2 = 1.5 cm.
= πr2 ( h + 2/3h ) h of cone = 2 cm
= 22/7 × 1.5 × 1.5 ( 8 + 2/3 ×2 ) h of cylinder = h of the model - h of 2 cones
= 22/7 × 2.25 ( 8 + 4/3 ) = 12 - 2(2) = 12 - 4 = 8 cm.
= 22/7 × 7.5 ( 24 + 4 )
= 22/7 × 7.5 ( 28 )
= 22 × 7.5 × 4
= 88 × 7.5
= 66 cm3...
Given:-
- The diameter of the model is 3 cm and its length is 12 cm.
- The each cone has a height of 2 cm.
To find:-
- Find the volume of air contained in the model that Rachel made...?
Solutions:-
- Height (h1) of each conical part = 2cm.
- Height (h2) of cylindrical part = 12 - 2 × height of conical part.
= 12 - 2 × 2
= 12 - 4
= 8cm
Radius (r) of cylindrical part = Radius of conical part = 3/2 cm.
Volume of air present in the model = Volume cylinder + 2 × Volume of cone.
=> πr²h2 + 2 × 1/3 πr²h
=> π (3/2)² + (8) + 2 × (1/3)² (2)
=> π × 9/4 × 8 + 2/3 × π × 9/4 × 2
=> π × 9 × 2 + 3π
=> 18π + 3π
=> 21π
=> 21 × 22/7
=> 3 × 22
=> 66cm³
Some Important:-
- Volume of cylinder ( Area of base × height ). = (πr²) × h
= πr²h
- Curved surface = ( Perimeter of base ) × height.
= (2πr) × h
= 2πrh
- Total surface are = Area of circular ends + curved surface area.
= 2πr² + 2πrh
= 2πr(r + h)
Where,
r = radius of the circular base of the cylinder.
h = height of cylinder.