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2 Answers
Feb 3, 2018

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#

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