175k views
4 votes
g the volume of a cube is increase at a rate of 5 cm^3/min. how fast is the surface area increasing when the lenght of an edge is 16 cm

User Eitan K
by
9.0k points

1 Answer

2 votes

Explanation:

the volume of the cube at the beginning is

edge³ = 16³ = 4096 cm³

after 1 minute it is 4101 cm³

that means the edge is then

cubic root(4101) = 16.00650777... cm

the surface area of a cube is

6×edge²

at the beginning it was

6×16² = 1536 cm²

after 1 minute (and the increased volume) it is

6×16.00650777...² = 1,537.249746... cm²

at that moment the surface area is increasing at

1.249745825... cm²/ minute

User Rodney Amato
by
7.8k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories