If the volume of a cube is increased by a factor of 10 (so that the new volume is 10 times the size of the original volume), by

Question

1 month ago

13

what factor does the surface area of the cube change?

1 answer:

PIT_PIT [12.4K] · Answer 1 · 2026-02-23T14:24:57+03:00

Answer:

surface area of the cube $10^{\frac{2}{3} }$ time

Step-by-step explanation:

Given information

The new volume equals 10 times that of the original volume

To discover

How the surface area is affected

Solution

Let's denote the side length of the cube as a

And its corresponding volume as V

Assuming a equals 2

Then the volume will be v1 = a³ = 2³ = 8

The surface area becomes 6a² = 6(2)² = 24..........1

So if the volume grows 10 times

Then

V = 10 × v1

a³ = 10 × 8

a³ = 80

a = 2 × ∛10

Consequently, the surface area increases to

Surface area = 6a²

Surface area = 6(2 × ∛10)²

Surface area = 24 × $10^{\frac{2}{3} }$ ............2

Thus, from equations 1 and 2

surface area / surface area = 24 × $10^{\frac{2}{3} }$ / 24

surface area = $10^{\frac{2}{3} }$

This indicates that the surface area of the cube will scale by $10^{\frac{2}{3} }$ time