Worksheet: Surface Areas of Composite Solids

In this worksheet, we will practice finding the surface area of a composite solid using the formulas for lateral or total surface areas of a single solid.

Q1:

The given figure is made by placing a cube of side length 13 cm on the top of another cube of side length 18 cm. Find its surface area.

Q2:

If a part of a cube, whose edge length is 7 cm, is cut to form a cuboid with side lengths of 3 cm, 4 cm, and 4 cm, find the surface area of the remaining part of the cube.

Q3:

The object shown is made from two cubes, one of side 3.3 cm, and the other 1.2 cm. If you must paint this object, what area do you report?

Q4:

A room has a floor in the shape of a square of side 5 m. Its walls are 3 m high, and it has door that is 87 cm wide and 2.1 m high. It also has two windows, each 90 cm by 51 cm. What is the cost of painting the walls and ceiling at a cost of 11 LE per square metre? Give your answer to the nearest hundredth.

Q5:

Work out the surface area of the prism.

  • A120 unit
  • B94 unit
  • C60 unit
  • D40 unit
  • E76 unit

Q6:

The buoy below is made of two right circular cones on a common base of radius 27 cm. If the cost of an erosion resistant coat is 300 LE per square metre, find, to the nearest tenth, the cost of painting the buoy.

Q7:

This shape is composed of a cylinder and a hemisphere. Find the surface area of the shape leaving your answer in terms of 𝜋.

  • A 2 2 0 𝜋 cm2
  • B 1 7 8 . 3 3 𝜋 cm2
  • C 1 9 5 𝜋 cm2
  • D 1 7 0 𝜋 cm2
  • E 2 4 5 𝜋 cm2

Q8:

Ethan cut a right-triangular prism from the center of a cylinder that had a radius of 6 cm and a height of 20 cm as illustrated. Calculate, to 2 decimal places, the surface area of the resulting shape.

Q9:

This shape is composed of a rectangular prism and a right square pyramid. Calculate the surface area of the shape. If necessary, round your answer to 2 decimal places.

Q10:

This model is formed of a pyramid on top of a prism, and its total height is 22 inches. Which has a greater surface area, the prism or the pyramid?

  • Athe pyramid
  • Bthe prism

Q11:

The buoy below is made of two right circular cones on a common base of radius 48 cm. If the cost of an erosion resistant coat is 300 LE per square metre, find, to the nearest tenth, the cost of painting the buoy.

Q12:

The object shown is made from two cubes, one of side 5.8 cm, and the other 2.5 cm. If you must paint this object, what area do you report?

Q13:

The object shown is made from two cubes, one of side 6.4 cm, and the other 3.1 cm. If you must paint this object, what area do you report?

Q14:

A room has a floor in the shape of a square of side 3 m. Its walls are 3.2 m high, and it has door that is 93 cm wide and 2.1 m high. It also has two windows, each 90 cm by 59 cm. What is the cost of painting the walls and ceiling at a cost of 8 LE per square metre? Give your answer to the nearest hundredth.

Q15:

If a part of a cube, whose edge length is 17 cm, is cut to form a cuboid with side lengths of 7 cm, 8 cm, and 11 cm, find the surface area of the remaining part of the cube.

Q16:

Answer the following questions for the prism shown.

Work out the volume of the prism.

Work out the surface area of the prism.

Q17:

Emma is baking cakes. She will make two cakes using a cake tin that has a depth of 4 inches and a diameter of 20 inches. Both cakes have the same depth as the tin. She will cut a circular hole with a diameter of 6 inches from the center of one of the cakes. The two cakes are modeled in the diagram.

She wants to cover the top and sides of cake A in frosting. What is the total surface area of the cake that will be covered in frosting? Give your answer to the nearest square inch.

What is the volume of cake B? Give your answer to the nearest cubic inch.

She wants to cover the top and sides of cake B in frosting, including the sides of the hole which she cut out. What is the total surface area of the cake that will be covered in frosting? Give your answer to the nearest square inch.

It costs $3.98 to buy a pack of frosting to cover 150 square inches of cake. How much money must Emma spend in total to frost both of the cakes?

What is the volume of cake A, to the nearest cubic inch?

If one container of frosting costs $3.98 and covers 150 square inches of cake. How much money must Emma spend in total to frost both of the cakes?

Q18:

The shape in the figure needs to be wrapped in paper. Work out the minimum area of paper that would be needed to completely cover the shape.

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