Question

HURRYi
Jayne stacked two cubes on top of each other as shown. The edge length of the smaller cube is half the edge length of the cube below what is the surface area of the new figure?

Answer 1

The surface area of the new figure is 1470 square meters, if the edge length of the smaller cube is half the edge length of the cube below and edge length of bottom cube is 14 m.

Step-by-step explanation:

The given is,

         Length of Bottom (larger) cube is 14 meters

Step:1

      Surface area of new figure = (Surface area of smaller cube) +  

                                             (Surface area of bottom (larger) cube)....(1)

Step:2

        Surface area of Bottom(larger) cube is,

                             $Surface area, A = 6a^{2}$..............................................(2)

        From given, a = 14 m

        Equation (2) becomes,

                                                                  $=6(14)^{2}$

                                                                  $=(6)(196)$

                                                                   $=1176$

              Surface area of bottom cube, A = 1176 square meters

Step:3

           Surface area of smaller (top) cube is,

                         $Surface area, A = 6a^{2}$....................................................(3)

             From given, a = 7 m                   ( ∵ The edge length of the smaller cube is half the edge length of the cube below)

             Equation (2) becomes,

                                                                  $=6(7)^{2}$

                                                                  $=(6)(49)$

                                                                   $=294$

              Surface area of bottom cube, A = 294 square meters

Step:4

        From equation (1),

                      Surface area of new figure = 1176 + 294

                                                                    = 1470

                      Surface area of new figure = 1470 square meters

Result:

           The surface area of the new figure is 1470 square meters, if the edge length of the smaller cube is half the edge length of the cube below and edge length of bottom cube is 14 m.

Answer 2

The surface area of the new figure is 1421 square meters

How to determine the surface area

The surface area of a cube is:

$A = 6l^2$

The side length of the big cube is 14 m.

So, the surface area is:

$A_1 = 6 * 14^2$

$A_1 = 1176$

The side length of the small cube is 7 m.

So, the surface area of the visible sides of the small cube is:

$A_2 = (6 -1) * 7^2$

$A_2 = 245$

The surface area of the shape is then calculated as:

$A = A_1 + A_2$

This gives

$A = 1176 + 245$

$A = 1421$

Hence, the surface area of the new figure is 1421 square meters

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