If each edge of a cube is increased by 30 then what is the percentage increase in the volume of cube

Solution:

Let the initial edge of the cube be 'l' cm.

If each edge of the cube is doubled, then it becomes '2l' cm.

(i) Initial surface area = 6 l²

New surface area = 6(2l)² = 6 × 4 l² = 24 l²

Ratio = 6 l² : 24 l² = 1:4

Thus, the surface are increases by 4 times

(ii) Initial volume of the cube = l³

New volume = (2l)³ = 8 × l³

Ratio = l³: 8 l³= 1:8

Thus, the volume increases by 8 times

☛ Check: NCERT Solutions for Class 8 Maths Chapter 11

Video Solution:

Maths NCERT Solutions Class 8 Chapter 11 Exercise 11.4 Question 7

Summary:

If each edge of a cube is doubled, (i) the surface area increases by four times (ii) the volume of the cube increases by eight times.

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Recall that the the volume of a cube is

So the new volume is

So "If each edge of a cube is increased by 30%", then the volume increases by 219.7%