Question

Two cardboard boxes are stacked on top of each other. The top box is a cube with sides of 10 in. The bottom box is a rectangular prism with a length of 20 in, width of 15 in, and height of 8 in. Find the surface area of the composite shape. Select the correct answer.
A. 1,605 in²
B. 1,506 in²
C. 1,560 in²

Answer 1

The surface area of the composite shape is 1560 square inches

Step-by-step explanation:

The surface area of the top cardboard is,

SA = 5 x area of each side

Because one side is attached with another cardboard box . So while finding the area only 5 sides are calculated.

SA = 5 ( 10 x 10)

  = 500 square inches

The surface area of the rectangular prism cardboard,

Given that,

l = 20 in

w =15 in

h = 8 in

A = 2(lw + wh + hl) - 100

We are subtracting 100 because it is the area of one side of the square cardboard box on top of the rectangular prism box .

A = 2(300 + 120 + 160) - 100

= 2(580) - 100

= 1160-100

= 1060 square inches

Total surface area = SA + A

= 500 + 1060

= 1560 square inches

Answer 2

The surface area of composite shape is 1760 square inches, if two cardboard boxes are stacked on top of each other. The top box is a cube with sides of 10 in and the bottom box is a rectangular prism with a length of 20 in, width of 15 in, and height of 8 in.

Step-by-step explanation:

The given is,

                The top box is a cube with sides of 10 in

                The bottom box is a rectangular prism with a length of 20 in, width of 15 in, and height of 8 in.

Step:1

      Surface area of composite figure = Surface area of cube +

                                                                  Surface area of rectangular prism

Step:2

        Formula for surface area of cube,

                                $Surface area cube, A _{Cube} = 5a^{2}$

        ( Only 5 sides area considered )

        Where, a - Side of cube

       From given, a = 10 inches

       From the surface area equation,

                                  $A_{Cube} = 5 (10)^{2}$

                                             = (5)(100)

                                             = 500

         Surface area of cube = 500 square inches

Step:3

          Formula surface area of rectangular prism,

                          $A _{rectangular prism} = 2 (wl+lh+hw)-100$

         Where, w - Width

                      l - Length

                      h - Height

         From the given values.

                     w = 15 inches

                       l = 20 inches

                      h = 8 inches

         Surface area equation becomes,

                      $A _{rectangular prism} = 2 ((20)(15)+(20)(8)+(8)(15))-100$

                                                 = 2 ( 300 + 160 + 120 )-100

                                                 = 2 (580)-100

         Surface area of rectangular prism = 1060 square inches

         From the step 1,

              Surface area of composite shape = 500+1060

                                                                        = 1560 square inches

Result:

        The surface area of composite shape is 1560 square inches.