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Worksheet: Surface Area of a Rectangular Prism

Q1:

Given that a cube has a surface area of 234 ft2, determine the area of one of its faces.

Q2:

If the perimeter of the base of a cube is 54.4 cm, find its total surface area.

Q3:

What is the difference in surface area between a cube with an edge length of 16 inches and a cube with an edge length of 5 inches?

Q4:

What is the surface area of a cube whose total edge length is 36 cm?

  • A 18 cm2
  • B 36 cm2
  • C 9 cm2
  • D 54 cm2

Q5:

Find the surface area of this shape.

Hint: You can draw the net of the shape to help you.

Q6:

Madison wants to wrap a birthday gift for a friend. The gift is in a rectangular prism shaped box which is 4 inches wide, 10 inches long, and 3 inches high. The table shows the different options for purchasing wrapping paper. Madison needs enough paper to wrap the whole gift, but does not want to have a lot of paper left over. Which choice would you recommend to Madison?

Paper A Paper B Paper C Paper D
163 square inches 124 square inches 168 square inches 88 square inches
  • A paper B
  • B paper A
  • C paper D
  • D paper C

Q7:

The sides of three cubes are in the ratio 5 6 4 . What is the ratio of their lateral surface areas?

  • A 5 6 4
  • B 1 2 5 2 1 6 6 4
  • C 2 5 3 6 8
  • D 2 5 3 6 1 6

Q8:

Work out the surface area of the rectangular prism shown.

Q9:

Given that the sum of the edge lengths of a cube is 91.2 cm, find its lateral surface area and its surface area.

  • Alateral surface area = 3 6 4 . 8 c m 2 , surface area = 5 4 7 . 2 c m 2
  • Blateral surface area = 5 1 9 . 8 4 c m 2 , surface area = 7 7 9 . 7 6 c m 2
  • Clateral surface area = 2 3 1 . 0 4 c m 2 , surface area = 2 8 8 . 8 c m 2
  • Dlateral surface area = 2 3 1 . 0 4 c m 2 , surface area = 3 4 6 . 5 6 c m 2
  • Elateral surface area = 6 0 . 8 c m 2 , surface area = 9 1 . 2 c m 2

Q10:

Mason’s mom told him she would buy him paint so he could paint his room. He just needs to tell her how much paint to buy. Mason takes measurements of his room. The length of the room is 9 meters, the width of the room is 8 meters, and the height (floor to ceiling) is 3.5 meters. To paint the four walls of his room, how many square meters need to be painted?

Q11:

A rectangular piece of cardboard of length 25 cm and width 14 cm, is being made into a box. A square of side length 4 cm is cut out of the cardboard at each corner. The remaining part is folded into a rectangular prism. Find the surface area of the rectangular prism.

  • A 350 cm2
  • B 102 cm2
  • C 388 cm2
  • D 286 cm2

Q12:

A box without a lid has length, width, and height 2.4 m, 1 m, and 70 m respectively. What is the cost of covering the inside with iron sheets at a cost of 6 LE per square metre?

Q13:

Find the lateral and total area of the shape below after being folded, and approximate the result to the nearest hundredth.

  • Alateral area = 6 1 5 . 0 4 c m 2 , total area = 1 9 0 6 . 6 2 c m 2
  • Blateral area = 9 2 2 . 5 6 c m 2 , total area = 6 1 5 . 0 4 c m 2
  • Clateral area = 1 9 8 . 4 c m 2 , total area = 2 9 7 . 6 c m 2
  • Dlateral area = 6 1 5 . 0 4 c m 2 , total area = 9 2 2 . 5 6 c m 2

Q14:

Sophia wants to wrap a cube-shaped gift box that has a side length of 20 inches. How much paper does she need?

Q15:

If the sum of the edge lengths of a cuboid is 152 cm, and the ratio between its length, width, and height is 8 3 8 , find its surface area.

Q16:

What is the ratio of the area of one face of a cube to its lateral area?

  • A 3 2
  • B 1 6
  • C 1 4

Q17:

Determine the lateral surface area and the surface area of a cube whose edge length is 3.7 cm.

  • Alateral surface area = 5 9 . 2 c m 2 , surface area = 8 8 . 8 c m 2
  • Blateral surface area = 8 2 . 1 4 c m 2 , surface area = 5 4 . 7 6 c m 2
  • Clateral surface area = 5 4 . 7 6 c m 2 , surface area = 6 8 . 4 5 c m 2
  • Dlateral surface area = 5 4 . 7 6 c m 2 , surface area = 8 2 . 1 4 c m 2
  • Elateral surface area = 2 9 . 6 c m 2 , surface area = 4 4 . 4 c m 2

Q18:

The lateral surface area of a cube is 4 cm2. Find the surface area and the volume of this cube.

  • A 4 cm2, 1 cm3
  • B 1 cm2, 6 cm3
  • C 6 cm2, 2 cm3
  • D 6 cm2, 1 cm3

Q19:

An open-topped box has the shape of a cube. If its lateral surface area is 82.3 cm2, what is the surface area of its faces, to the nearest hundredth?

Q20:

What is the ratio between the lateral area and the total area of a cube?

  • A 4 9
  • B 3 2
  • C 2 3

Q21:

The side length of a cube is the same as the side length of an equilateral triangle with perimeter 19.5 cm. What is the lateral surface area of the cube?

Q22:

A metallic cube with surface area 726 cm2 is melted and reshaped into a rectangular prism with base 16 cm by 15 cm. Find the surface area of the rectangular prism to the nearest hundredth, if needed.

  • A 667.55 cm2
  • B 343.84 cm2
  • C 726 cm2
  • D 823.84 cm2

Q23:

Work out the surface area of a cube with a side length of 5 inches.

Q24:

A cuboid-shaped water tank of height 2 m has a base with perimeter 28 m. If its base dimensions are in the ratio 3 4 , find the cost of painting the outer surface of the tank (excluding the base) at a costs of 9 LE per square metre.

Q25:

The surface area of a cube is 1 020 cm2. What is the area of one face of the cube?

  • A 340 cm2
  • B 255 cm2
  • C 85 cm2
  • D 170 cm2