What is the length of a side of a cube where the surface area equals its volume in magnitude?
Answers
Answer:
The surface area of anything can’t be equal to its volume even if the numbers look the same, because the units of area and volume are different.
Nonetheless, the number you are looking for is probably the length of an edge ( not the “side”).
The surface area of a cube is:
A = 6s x s
The volume of a cube is:
V = s x s x s
For A to equal V numerically s must equal 6.
But it is kind of a meaningless answer.
Step-by-step explanation:
Algebraically there are two possible answers but only one of them is logical we should eliminate the other using logical thinking.
Lets first find those two:
let the length of the side be x,
there are 6 faces in a cube so we get:
x^3=6(x^2)
one answer is to just cancel out x^2 from both sides to get x=6,
The other possible solution is x=0.
Why? Simply because its a value of x that makes the above equation true. (Go ahead and substitute 0 for x, you’ll get 0=0 which is a true equation.)
Now here’s the tricky but interesting part. Anyone would dismiss 0 as the illogical answer and choose 6 as correct. But it’s actually the other way around.
There are times where math and logic clash, but here, algebra does give us the answer, ZERO, we just need some intuition. The answer “A SIDE WITH LENGTH ZERO” (whatever unit) actually means “THERE IS NO SUCH CUBE!”
Think about it. Can volume ever be equal to surface area in any solid? NO. They are two different quantities. Its like asking if the gas pressure and light intensity can be equal in a room, you can’t consider the numbers while ignoring the units candela and pascal (You can think of an example more familiar to you).