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Exploring Shapes and Space

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Exploring Shapes and Space

Use geometry to plan a mini-golf hole. Show your working and include units where needed. Diagrams are not drawn to scale unless stated.

Shape and Space Clues

Solve the clues to identify and describe shapes.

1.A mini-golf obstacle has 2 triangular faces and 3 rectangular faces. What 3D shape is it, and how many faces does it have altogether?

2.A circular tunnel has one curved surface and two flat circular ends. Which solid is it?

Cone
Cylinder
Sphere
Triangular prism

3.The top-down outline of a putting green is a rectangle measuring 8 m by 5 m. Find its perimeter and area.

4.A square tile has side length 1.5 m. What is its area?

Angles and Transformations

Use angle facts and coordinate movement to plan the course.

5.At a turning point, two angles on a straight line are 127° and x°. Find x.

6.A triangular sign has angles of 48° and 67°. Calculate its third interior angle.

7.On a coordinate grid, a marker is at A(2, 1). It is translated 4 units right and 3 units up. What are its new coordinates?

8.A triangular course marker has vertices (1, 1), (4, 1) and (1, 3). Reflect it in the y-axis. Write the coordinates of the reflected vertices.

Build and Explain

Finish the design challenge with clear reasoning.

9.A rectangular prism-shaped obstacle is 2 m long, 1.5 m wide and 0.8 m high. Find its volume.

10.A circular obstacle has radius 3 m. Using π ≈ 3.14, calculate its circumference. Give your answer to 1 decimal place.

11.A design uses a 90° anticlockwise rotation about the origin. State two properties that stay the same under this rotation, and explain what happens to the position of each point.