Hi guys please solve this question-
Rachel, an engineering student, was asked to make a model shaped like a cylinder with two cones attached at its two ends by using a thin aluminum sheet. The diameter of the model is 3 cm and its length is 12 cm. If each cone has a height of 2 cm, find the volume of air contained in the model that Rachel made. (Assume the outer and inner dimensions of the model to be nearly the same)
Answers
Answer:
volume of air contained in the model = volume of cylinder+ 2*volume of cone
Step-by-step explanation:
volume of cylinder= 22/7 * 1.5^2 * 12-4
=22/7* 15/10 * 15/10 * 8
= 42.28 cubic cm approx.
volume of cone = 1/3 * 22/7 * 1.5^2 * 2
=33 cubic cm
volume of 2 cones =66 cubic cm
total air contained = 42.28 + 66
= 108.28 cubic cm approx.
Volume of Air Contained in Model
= Volume of Model
= Volume of Cylinder + Volume of 1st cone + Volume of 2nd Cone
= πr²h + 1/3πr²h + 1/3πr²h
= (π × r² × h) + (1/3 × π × r² × h) + (1/3 × π × r² × h)
= (22/7 × (3/2)² × h) + (1/3 × 22/7 × (3/2)² × h) + (1/3 × 22/7 × (3/2)² × h)
= (22/7 × 9/4 × h) + (1/3 × 22/7 × 9/4 × 2) + (1/3 × 22/7 × 9/4 × h)
= (198/28 × h) + (22/217 × 9/4 × h) + (22/21 × 9/4 × h)
= (198/28 × (12 - 4)) + (22/21 × 9/4 × 2) + (22/21 × 9/4 × 2)
= (198/28 × 8) + (22/21 × 9/4 × 2) + (22/21 × 9/4 × 2)
= (198/28 × 8) + (22/21 × 9/2 × 1) + (22/21 × 9/2 × 1)
= (198/28 × 8) + (22/21 × 9/2) + (22/21 × 9/2)
= (1584/28) + (198/42) + (198/42)
= (56.57) + (4.71) + (4.71)
= 65.99 cm³
≈ 66 cm³