Question

Three same-sized cubes are attached to the top of a rectangular prism as shown below. If a = 9 cm, b = 24 cm, and c = 3 cm, what is the surface area of the figure? A. 945 square centimeters B. 1,134 square centimeters C. 1,188 square centimeters D. 1,161 square centimeters

Answer 1

you need to provide the prism

Answer 2

1134

Explanation:

Since the three cubes are the same size, the area of each square face of the cubes is 3 cm × 3 cm = 9 sq cm.

Since the cubes are attached to the top of the rectangular prism, some faces are not exposed. So, the non-exposed faces are not included when calculating the surface area.

Each cube has 5 square faces exposed, and the rectangular prism has 2 square faces and 4 rectangular faces exposed, minus parts of the top rectangle.

First, calculate the surface area of the three cubes.

SAcubes = 3[5 faces]

= 3[5(9 sq cm)]

= 3[45 sq cm]

= 135 sq cm

Next, calculate the surface area of the rectangular prism.

SArect = 2 square faces + 4 rectangular faces - 3 parts

= 2(9 cm)(9 cm) + 4(9 cm)(24 cm) - 3(9 sq cm)

= 162 sq cm + 864 sq cm - 27 sq cm

= 999 sq cm

Finally, calculate the total surface area of the figure.

SAtotal = cubes + rectangular prism

= 135 sq cm + 999 sq cm

= 1,134 sq cm

Therefore, the surface area of the figure is 1,134 square centimeters.