Question

Help pleaseeeeeeeeeeee ?

Answer 1

C. `3150 "cm"^2`

Explanation:

Suppose there was no hole. What would the surface area be?

• There are two rectangular faces with sides `x` and `y`, so area `xy`.

• There are two rectangular faces with sides `y` and `z`, so area `yz`.

• There are two rectangular faces with sides `z` and `z`, so area `zx`

So the total surface area would be `2xy+2yz+2zx`

When we make an `x xx x xx x` cube shaped hole, we remove two squares of area `x^2` and add four new squares of area `x^2`. So the net change is `+2x^2`.

So the total surface area in `"cm"^2` of the rectangular prism with hole is:

`2xy+2yz+2zx+2x^2`

`=2(5)(40)+2(40)(30)+2(30)(5)+2(5)^2`

`=400+2400+300+50`

`=3150`

Answer 2

The requested surface area is

`E=2*(x*y+y*z+z*z)+2*x^2`

Hence the answer by substituting the values of x,y,z

is

`E=3150`

The correct answer is C