Worksheets · Higher

Area and volume in similar figures

3 exam-style questions. Answers and the mark for each step are on the last page.

1. Question 1Non-calculator · 3 marks

   Two cylinders are mathematically similar. The smaller has height 6 cm and volume $160\text{ cm}^3$. The larger has height 9 cm.

   (a) Work out the volume of the larger cylinder. (3)
2. Question 2Non-calculator · 4 marks

   Two solid shapes are mathematically similar. Their surface areas are $72\text{ cm}^2$ and $162\text{ cm}^2$. The smaller shape has volume $96\text{ cm}^3$.

   (a) Work out the volume of the larger shape. (4)
3. Question 3Non-calculator · 4 marks

   A solid cone is cut by a plane parallel to its base, one third of the way down from the vertex (measured along the height). This cuts off a small cone and leaves a frustum.

   (a) Show that the ratio of the volume of the small cone to the volume of the frustum is $1 : 26$. (4)