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Help pleaseeeeeeeeeeee ?

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Answer 1 · 2018-02-03T00:44:02

C. $3150 {cm}^{2}$ $3150 "cm"^2$

Explanation:

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

There are two rectangular faces with sides $x$ $x$ and $y$ $y$ , so area $x y$ $xy$ .
There are two rectangular faces with sides $y$ $y$ and $z$ $z$ , so area $y z$ $yz$ .
There are two rectangular faces with sides $z$ $z$ and $z$ $z$ , so area $z x$ $zx$

So the total surface area would be $2 x y + 2 y z + 2 z x$ $2xy+2yz+2zx$

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

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

$2 x y + 2 y z + 2 z x + 2 x^{2}$ $2xy+2yz+2zx+2x^2$

$= 2 (5) (40) + 2 (40) (30) + 2 (30) (5) + 2 {(5)}^{2}$ $=2(5)(40)+2(40)(30)+2(30)(5)+2(5)^2$

$= 400 + 2400 + 300 + 50$ $=400+2400+300+50$

$= 3150$ $=3150$

Answer 2 · 2018-02-03T00:47:44

The requested surface area is

$E = 2 \cdot (x \cdot y + y \cdot z + z \cdot z) + 2 \cdot x^{2}$ $E=2*(x*y+y*z+z*z)+2*x^2$

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

is

$E = 3150$ $E=3150$

The correct answer is C

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