Consider the volumes of the following: 1. A parallelepiped of length 5 cm, breadth 3 cm and height 4 cm 2. A cube of each side 4 cm 3. A cylinder of radius 3 cm and length 3 cm 4. A sphere of radius 3 cm The volumes of these in the decreasing order is

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Q: 20 (IAS/2002)
Consider the volumes of the following:
1. A parallelepiped of length 5 cm, breadth 3 cm and height 4 cm
2. A cube of each side 4 cm
3. A cylinder of radius 3 cm and length 3 cm
4. A sphere of radius 3 cm The volumes of these in the decreasing order is

question_subject: 

Maths

question_exam: 

IAS

stats: 

0,3,7,0,5,2,3

keywords: 

{'volumes': [0, 0, 1, 0], 'sphere': [2, 0, 8, 5], 'cube': [0, 0, 2, 0], 'cylinder': [0, 2, 1, 2], 'radius': [0, 0, 2, 2], 'breadth': [1, 2, 1, 1], 'length': [0, 0, 1, 0], 'height': [0, 0, 1, 2], 'iv': [6, 110, 77, 8]}

To determine the volumes of the given shapes and arrange them in decreasing order, let`s calculate the volumes of each shape:

1. Parallelepiped: The volume of a parallelepiped is given by the formula V = length x breadth x height. Plugging in the given values, we get V = 5 cm x 3 cm x 4 cm = 60 cm³.

2. Cube: The volume of a cube is given by the formula V = side³. Plugging in the given value of side (4 cm), we get V = 4 cm x 4 cm x 4 cm = 64 cm³.

3. Cylinder: The volume of a cylinder is given by the formula V = ?r²h, where r is the radius and h is the height. Plugging in the given values, we get V = ? x (3 cm)² x 3 cm = 27? cm³ (approximately 84.78 cm³).

4. Sphere: The volume of a sphere is given by the formula V = (4/3)?r³. Plugging in the given value of radius (3 cm), we get V = (4/3) x ? x (3 cm)³ = 36? cm³ (approximately 113.1 cm³).

Now, arranging the volumes in decreasing order, we have:

IV (Sphere), III (Cylinder), II (Cube), I (Parallelepiped).

Therefore, the correct answer is: IV, III, II, I.