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Lesson Worksheet: Surface Areas of Composite Solids Mathematics • 7th Grade

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 (including the base of the combined solid), 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 pound, 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.

  • A220𝜋 cm2
  • B178.33𝜋 cm2
  • C195𝜋 cm2
  • D170𝜋 cm2
  • E245𝜋 cm2

Q8:

Liam 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

This lesson includes 2 additional questions and 54 additional question variations for subscribers.

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