Shape and Space: Going Further
Composite solids, and reasoning between scale factor, area and volume ratios.
8 questions, free, marked as you go with a worked explanation on every one.
What this covers
- volume surface area similarity
The questions
- A cylinder has radius 4 cm and height 10 cm. A cone with the same radius and height sits on top of it, forming a silo shape. Find the total volume of the silo, to the nearest whole number, in cubic centimetres. (Use π ≈ 3.14.)
- Two similar solids have a volume ratio of 27 to 1. What is the ratio of their surface areas?
- A cone has radius 6 cm and slant height 10 cm. Find its lateral surface area, to the nearest whole number, in square centimetres. (Use lateral surface area = π r l and π ≈ 3.14.)
- A map is drawn at a scale where every centimetre on the map represents fifty thousand of the same unit in real life. A road on the map is 6 cm long. How long is the actual road, in kilometres?
- A cube has surface area 96 square centimetres. What is its volume, in cubic centimetres?
- A sphere is enlarged so that its radius doubles. By what factor does its volume increase?
- Two similar triangles have corresponding sides in the ratio 3 to 5. The smaller triangle has perimeter 18 cm. Find the perimeter of the larger triangle, in centimetres.
- A cylinder's height is doubled while its radius stays the same. By what factor does its volume increase?