The outside of the rectangular box represented in the figure

Top = 25*10 = 250
Sides = 5*10*2 = 100
Front & Back = 25*5*2 = 250

Total = 600
Answer is B

basically its an application of the 3D rectangle formula?

Yes... The shape is called a cuboid. We are not considering the bottom in this case.

total area of cuboid - area of bottom of cuboid = paper required to wrap all sides except bottom of the cuboid

total area of cuboid = area of top and bottom side faces (l*b)+area of two side faces(h*b) + area of two side faces (l*h) = 2*25*10 + 2*5*10 + 2*25*5 = 500+100+250=850

area of bottom face = 250

so paper needed = 850 - 250 = 600 sqinches

even immediately after finishing reading the question, we know how to solve the problem. this one takes on more than 90 seconds to get to the correct choice.
practice a lot is good

How do we know not to multiply 25 x 10 twice

Hey All,

Its super basic but I'm having trouble in translating top/bottom/sides wording into length, width and height. As the general formula for the surface area of a cuboid/rectangular solid is 2(lw+wh+lh), how can we translate this into top/bottom/sides etc.?

Thanks!

We have been told specifically that the bottom is not to be covered. Hence we don't multiply 25*10 by 2.
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The length, width and height changes according to the orientation of the box. The height right now is 5 inches but if you turn it 90 degrees, it could be 25 inches. But the overall surface area and volume stays the same irrespective of what you consider as length, breadth and height. Hence the formulas are symmetrical:
Surface Area = 2*(lb + bh + hl)
Volume = lbh

If you interchange l and b, the formula stays the same. So it doesn't really matter what you take as length breadth and height.

In this question, they have specified the orientation of the box and hence the face which is lying at the bottom. That face is the one which has area of 25*10.

Hence the surface area of the rest can be calculated as 2*(25*10 + 10*5 + 5*25) - 25*10
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The top face has an area of 25 x 10 = 250 sq. in.

The front and back faces have a total area of (25 x 5) x 2 = 250 sq. in.

The right and left faces have a total area of (10 x 5) x 2 = 100 sq. in.

Therefore, we need 250 + 250 + 100 = 600 sq. in. of wrapping paper.

Answer: B
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Notice we only need to calculate five sides:

\(5 * 10 = 50 * 2 = 100\)

\(25* 5 = 125 * 2 = 250\)

\(25 * 10 = 250 = 250\)

\(250 + 250 + 100 = 600\)

Answer is B.

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