Question

the volume of a cube is increased by 700% by how much will its surface area increase​

Answer 1

Step-by-step explanation:

Given the volume of a cube is increased by 700% by how much will its surface area increase​

• So the volume of a sphere is V = 4/3 πr^3
• We have Surface area of sphere S = 4 πr^2
• Given volume of a cube is increased by 700%
• So Volume V1 and V2 will be the initial and final volume.
• Therefore V2 / V1 = 8  
•              Or 4/3 πr2^3 / 4/3 πr1^3 = 8
•             Or  r2^3 / r1^3 = 8
•            So (r2 / r1)^3 = 2^3
•             Or r2 / r1 = 2
•  Similarly S2/S1 = 4πr2^2 / 4 π r1^2
•                               = (r2 / r1)^2
•                                = (2)^2
•                                = 4
• Therefore S2 = 4 S1
• Or S2 – S1 = 3 S1
•                      = 300 %
• Therefore the increase in surface area is 300%

Reference link will be

https://brainly.in/question/23318726