Algebra Task 3: Mathematical investigation AC 3.1 Form equations. A cell exchanges materials with its environment to provide raw materials for cell processes and to remove waste products. The ratio of surface area to volume for a cell is a key factor in determining the efficiency of this exchange of materials. SAVR = surface area Part A d volume a. Modelling the cell as a cube, find the surface area to volume ratio (SAVR) for cells of the following sizes: d = 6 x 10-6 m d = 8 x 10-6 m d = 10 x 106 m b. Area of one face of the cube = d² Volume of cube = d³ Write a general formula for the SAVR of a cube of side d and use it to explain how SAVR changes with the size of the cube. (AC 3.1) C. Use the formula to find the value of d for which SAVR is equal to (i) 1000 m¹, (ii) 1000000 m. Part B a. Investigate the SAVR for different types of cell. It is up to you what shapes to investigate. Explain what you are doing at each stage. Remember this is an algebra unit (not a biology unit) so make sure you use algebra in your analysis. b. Write a paragraph to explain what you can conclude from your investigation.