Challenge-
Class - 10th,surface area and volume.
Q) 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.
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Answers
Given:-
- Height of cylinder = 12 – 4 = 8 cm
- Radius = 1.5 cm
- Height of cone = 2 cm
To Find:-
- the volume of air contained in the model that Rachel made.
step-by-step solution:-
Let r cm be the radius and h cm be the height of a cone, then
• r = 1.5 cm, and h = 2 cm,
Now, Volume of conical part = 1/3 πr²h
⟶ [1/3π × 1.5 × 1.5 × 2] cm²
⟶ 1.5π cm²
Let r cm be the radius and h cm be the height of the cylindrical part, then
• r1 = 1.5cm and h1 = 8cm.
Now, Volume of cylinderical part = πr1²h
⟶ [π × 1.5 × 1.5 × 8] cm³
⟶ 18π cm³
Hence,
the volume of air contained in the model that Rachel made
= Volume of two conical part + Volume of cylindrical part.
⟶ (2 x 1.5 π + 18 π) cm³
⟶ (3 π + 18 π) cm³
⟶ (21 π) cm³
⟶ [21 × 2 - 2/7 ] cm³
⟶ 66cm³
For the given statement first draw a diagram,
In this diagram, we can observe that
Height (h1) of each conical part =2 cm
Height (h2) of cylindrical part 12−2−2=8 cm
Radius (r) of cylindrical part = Radius of conical part = 23 cm
Volume of air present in the model = Volume of cylinder + 2× Volume of a cone
=πr2h2+2×πr2h1
=π(23)2×8+2×31π(23)2(2)
=π×49×8+32π×49×2
=18π+3π=21π
=21×722=66 cm2
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