Shape and Space: Further Practice
Similar figures, and the volume and surface area of spheres and cones.
8 questions, free, marked as you go with a worked explanation on every one.
What this covers
- volume surface area similarity
The questions
- Two similar triangles have a scale factor of 3 from the smaller to the larger. The smaller triangle has area 8 cm². What is the area of the larger triangle, in square centimetres?
- A sphere has radius 6 cm. Find its volume, to the nearest whole number. (Use V = 4/3 π r³ and π ≈ 3.14.)
- Two similar rectangular prisms have a linear scale factor of 2 from the smaller to the larger. What is the ratio of their volumes?
- A cone has radius 5 cm and height 12 cm. Find its volume, to the nearest whole number. (Use V = 1/3 π r² h and π ≈ 3.14.)
- Use the table below, giving the side length of two similar polygons. What is the scale factor from the smaller polygon to the larger one?
- Two similar cylinders have a scale factor of 3 from the smaller to the larger. The smaller cylinder has surface area 20 cm². What is the surface area of the larger one, in square centimetres?
- A model car is built at a scale of 1 to 20. The model is 8 cm long. How long is the real car, in centimetres?
- A sphere has radius 5 cm. Find its surface area, to the nearest whole number. (Use surface area = 4 π r² and π ≈ 3.14.)