The height of a cube of side a cm and a pyramid of height a cm has a square base of a cm. Find the ratio of their volume.
1. 1 : 3
2. 3 : 1
3. 2 : 3
4. 3 : 2
1. 1 : 3
2. 3 : 1
3. 2 : 3
4. 3 : 2
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Correct Answer – Option 2 : 3 : 1
Given :
Side of the cube = a cm
Area of base of pyramid = a2 cm2
Height of the pyramid = a cm
Formula used :
Volume of the cube = a3
Volume of the pyramid = (1/3) × (Area of base × height)
Calculations :
Volume of the cube = a3
Volume of the pyramid = (1/3) × (a2 × a) = (1/3)a3
Ratio of volume of cube to volume of pyramid = a3 : (1/3)a3
⇒ 3 : 1
∴ The ratio of the volume is 3 : 1