Worksheet Chapter 6: Three-Dimensional Geometric Shapes

1. Calculate the volume of a cuboid measuring 12 cm long, 5 cm wide, and 8 cm high.

2. Fill in the blank: The 2D layout pattern obtained by unfolding a 3D solid object is called a ________.

3. Which of the following is the correct formula for the total surface area of a closed cylinder with radius r and height h?

4. A metal cone with a radius of 6 cm and height of 14 cm is melted down and recast into a solid sphere. (a) Calculate the volume of the cone. (b) Calculate the radius of the newly formed sphere in cm, correct to 2 decimal places. (Take π = 227)

5. A right triangular prism has a right-angled triangular base with sides 6 cm, 8 cm, and 10 cm. If the height/length of the prism is 15 cm, calculate its total surface area.

6. A composite solid consists of a cylinder topped with a hemisphere of the same radius (7 cm). The total height of the composite solid is 17 cm. (a) Find the height of the cylinder part. (b) Calculate the total volume of the composite solid. (Take π = 227)

7. A solid sphere has a radius of 7 cm. Calculate its total surface area. (Take π = 227)

8. True or False: A cone has two vertices.

9. True or False: The volume of a cone is equal to one-third the volume of a cylinder with the same base radius and height.

10. A cone has a radius of 5 cm and a slant height of 13 cm. Calculate its perpendicular height.