Given below are two quantities named I and II. Based on the given information, you have to determine the relation between the two quantities. You should use the given data and your knowledge of Mathematics to choose among the possible answers.
Quantity I: If the diameter of the sphere is 42 cm then find the volume of the sphere?
Quantity II: If the side of the cube is 27 cm then find the volume of the cube?
1. Quantity I > Quantity II
2. Quantity I ≥ Quantity II
3. Quantity II > Quantity I
4. Quantity II ≥ Quantity I
5. Quantity I = Quantity II or Relation cannot be established
Correct Answer – Option 1 : Quantity I > Quantity II
Given:
Diameter of sphere = 42 cm
Then, Radius = 21
Formula:
Volume of sphere = 4/3 × π × R3
Calculation:
We know that –
Volume of sphere = 4/3 × π × R3 …….. (1)
Now,
Put all the given values in equation (1) then we get
Volume of sphere = 4/3 × 22/7 × (42/2)3
⇒ 4/3 × 22/7 × 21 × 21 × 21
⇒ 4 × 22 × 21 × 21
⇒ 38808
∴ The Volume of a sphere will be 38808 cm3
Quantity II:
Given:
Side of cube = 27 cm
Formula:
Volume of cube = (side)3
Calculation:
We know that –
Volume of cube = (side)3 …….. (1)
Now,
Put the given value in equation (1) then we get
Volume of cube = (27)3
⇒ 27 × 27 × 27
⇒ 19683
∴ The Volume of a cube will be 19683 cm3
Comparison of both the result:
∴ Quantity I > Quantity II