lancelot is wrapping a present.The box he is using is rectangular prism with a length of 18 inches,a width 10 inches,and height of 4 inches.Find how many square inches of paper he needs to wrap the entire box? complete answer please
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lancelot is wrapping a present.The box he is using is rectangular prism with a length of 18 inches,a width 10 inches,and height of 4 inches.Find how many square inches of paper he needs to wrap the entire box? complete answer please
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Answer:
The problem is asking for the number of square inches, which means, we need to compute for the area. And Jason will wrap a rectangular prism box, and a rectangular prism is a solid figure, we will need to compute for the surface area of the prism. To do that, we will add the area of all the faces of the prism. There are 3 pairs of congruent faces in a rectangular prism. The top face is congruent with the bottom face, front and back faces are congruent, and the two sides are also congruent with each other. (See attached photo).
Considering our given, we have the following dimensions: Front Back = 4in x 18 in Top = Bottom = 10in x 18in Side A = Side B = 4in * 10in
Since we want to know the areas, we will multiply the dimensions: Front Back 4in x 18 in = 72 sq. in Top = Bottom = 10in x 18in = 180 sq. in. Side A Side B = 4in x 10in = 40 sq. in.
Multiply each side by 2 since they come in pairs we have: Front Back = 4in x 18 in = 72 sq. in (2) 144 sq. in =
Top = Bottom = 10in x 18in = 180 sq. in. (2) = 360 sq. in
Side A Side B = 4in x 10in = 40 sq. in. (2) = 80 sq. in
Adding these areas, 144 sq in + 360 sq in
+80 sq in=584 sq.in.
Simplifying what we did into one formula, we have SA = 2 2(wl + wh + hl) Let us try to solve again the problem using this formula.
W = 10in L = 18in
H = 4in
SA = 2[(10in)(18in) + (10in)(4in) + (4in)(18in)] SA = 2[180 sq. in + 40 sq. in. + 72 sq. in] SA = 2(292 sq. in) SA = 584sq . in
Therefore, Jason needs 584 sq. in. of paper to wrap the whole box.
Hope that helps
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