Biology – Spring 2012 – 3 rd Qtr. Hour: 4 th Mr. Gibson Room 213

The volume of a “sphere” is calculated using the formula: Unit 4: Cell Support/Mitosis/Energy (c) Energy & Cellular Volumes/Surface Areas V S = (4/3) ∏ r ³ Where: ∏ = Pi = 3.14 r = radius = ½ diameter And the “units” used are cubed (to the power of “3”)

The area of a “sphere” is calculated using the formula: Unit 4: Cell Support/Mitosis/Energy (c) Energy & Cellular Volumes/Surface Areas A S = 4 ∏ r ² Where: ∏ = Pi = 3.14 r = radius = ½ diameter And the “units” used are squared (to the power of “2”)

The volume of a “cylinder” is calculated using the formula: Unit 4: Cell Support/Mitosis/Energy (c) Energy & Cellular Volumes/Surface Areas V c = ∏ r ² h Where: ∏ = Pi = 3.14 r = radius = ½ diameter H = height of the cylinder; And the “units” used are cubed (to the power of “3”)

The surface of a “cylinder” is calculated using the formula: Unit 4: Cell Support/Mitosis/Energy (c) Energy & Cellular Volumes/Surface Areas A c = 2∏ r ² + 2 ∏ r h Where: ∏ = Pi = 3.14 r = radius = ½ diameter H = height of the cylinder; And the “units” used are squared (to the power of “2”) Surface area is blue shaded area & grey area.

When studying cells in terms of division, size, and functions… Unit 4: Cell Support/Mitosis/Energy (c) Energy & Cellular Volumes/Surface Areas Surface area and volume have major impacts on cellular size “limits”. Bacillus bacteria

Unit 4: Cell Support/Mitosis/Energy (c) Energy & Cellular Volumes/Surface Areas Now pair up: Using your notes calculate the surface area of a capsule.

Unit 4: Cell Support/Mitosis/Energy (c) Energy & Cellular Volumes/Surface Areas Now pair up: Using your notes calculate the surface area of a capsule. Hint No. 1: There is a “sphere” component to the capsule. Can you “see” it? The outside halves add together to make ONE sphere

Unit 4: Cell Support/Mitosis/Energy (c) Energy & Cellular Volumes/Surface Areas Now pair up: Using your notes calculate the surface area of a capsule. Hint No. 2: There is a “cylinder” component to the capsule. Can you “see” it? The between the sphere halves is one cylinder.

Unit 4: Cell Support/Mitosis/Energy (c) Energy & Cellular Volumes/Surface Areas Any new uni-cellular organism or single “daughter” cell… Newly created single cell … will continue to “grow” in size until a “certain limit” is reached. Maximum sized single cell

Unit 4: Cell Support/Mitosis/Energy (c) Energy & Cellular Volumes/Surface Areas Even though a capsule’s VOLUME is in cubic units (nm³) and SURFACE AREA is in square units (nm²)… … when the number values themselves approach parity (1 : 1 ratio) the cell has reached its maximum size… (A capsule = V capsule ) eg 10 nm² = 10 nm ³ Maximum sized single cell … it must either “split” (divide) –or- “die”.

Unit 4: Cell Support/Mitosis/Energy (c) Energy & Cellular Volumes/Surface Areas The reason any new uni-cellular organism or single “daughter” cell will continue to grow in size until it reaches an upper size limit is due to two factors: Newly created single cell Maximum sized single cell Removal of waste materials Provide parts, energy & nutrients

Unit 4: Cell Support/Mitosis/Energy (c) Energy & Cellular Volumes/Surface Areas To make this easier to see “number-wise”: You are given a new daughter cell that is “sphere” shaped. It has a diameter of 1 nm at this point. 2-1/2 minutes later it has grown and its diameter is now 2 nm. The diameter will continue to grow by 1 nm every two & one-half minutes until it reaches its size limit. How long will that be? CA0110: Make a chart and list your different diameters and then calculate the related surface areas and then volumes. From these number calculate the Surface Area –to- Volume RATIO. When you reach essentially 1 : 1 you have reached your cell’s size limit.