Question

if each edge of a quadrupled (4times)
1. how many times will it's surface area increase?
2. how many times will it's volume increase?​

Answer 1

Answer:

1. 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.
2. Let the initial edge of the cube be 'l' cm.
4. If each edge of the cube is doubled, then it becomes '2l' cm.
6. (i) Initial surface area = 6 l²
8. New surface area = 6(2l)² = 6 × 4 l² = 24 l²
10. Ratio = 6 l² : 24 l² = 1:4
12. Thus, the surface are increases by 4 times
14. (ii) Initial volume of the cube = l³
16. New volume = (2l)³ = 8 × l³
18. Ratio = l³: 8 l³= 1:8
20. Thus, the volume increases by 8 times

Answer 2

Answer:

Brainliest

Brainliest

Step-by-step explanation:

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