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Cell Biology - Cell Theory

Grade 9IB

Review the key concepts, formulae, and examples before starting your quiz.

🔑Concepts

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The Cell Theory states three main principles: 1. All living organisms are composed of one or more cells. 2. The cell is the basic unit of life. 3. Cells arise from pre-existing cells.

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Functions of Life: All unicellular organisms must perform Metabolism, Response, Homeostasis, Growth, Reproduction, Excretion, and Nutrition (MRHGRENMRH GREN).

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Surface Area to Volume Ratio (SAV\frac{SA}{V}): As a cell grows, its volume (VV) increases faster than its surface area (SASA). This limits cell size because the SASA must be large enough to transport nutrients in and waste products out to support the metabolic demands of the VV.

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Exceptions to Cell Theory: Striated muscle fibers (contain multiple nuclei and are very long), Aseptate fungal hyphae (lack discrete cells and have continuous cytoplasm), and Giant Algae (AcetabulariaAcetabularia, which grows to large sizes up to 10cm10 cm while being a single cell).

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Units of measurement in microscopy: 1mm=103μm1 mm = 10^3 \mu m (micrometers) and 1μm=103nm1 \mu m = 10^3 nm (nanometers).

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Emergent Properties: Multicellular organisms show properties that emerge from the interaction of their cellular components; 'the whole is greater than the sum of its parts'.

📐Formulae

Magnification(M)=Image size(I)Actual size(A)Magnification (M) = \frac{Image\ size (I)}{Actual\ size (A)}

Actual size(A)=Image size(I)Magnification(M)Actual\ size (A) = \frac{Image\ size (I)}{Magnification (M)}

Surface Area to Volume Ratio=SAVSurface\ Area\ to\ Volume\ Ratio = \frac{SA}{V}

1mm=1,000μm=1,000,000nm1 mm = 1,000 \mu m = 1,000,000 nm

💡Examples

Problem 1:

A micrograph of a red blood cell shows a diameter of 42mm42 mm. If the magnification is ×6,000\times 6,000, calculate the actual diameter of the cell in micrometers (μm\mu m).

Solution:

A=IM=42mm6,000=0.007mm=7μmA = \frac{I}{M} = \frac{42 mm}{6,000} = 0.007 mm = 7 \mu m

Explanation:

To find the actual size, divide the image size by the magnification. Since the question asks for the answer in μm\mu m, convert the measurement from mmmm to μm\mu m by multiplying by 1,0001,000.

Problem 2:

Calculate the surface area to volume ratio for a cubic cell with a side length of 2μm2 \mu m.

Solution:

SA=6×(2μm)2=24μm2SA = 6 \times (2 \mu m)^2 = 24 \mu m^2 V=(2μm)3=8μm3V = (2 \mu m)^3 = 8 \mu m^3 Ratio=248=3μm−1\text{Ratio} = \frac{24}{8} = 3 \mu m^{-1}

Explanation:

The surface area of a cube is 6L26L^2 and the volume is L3L^3. Dividing the surface area by the volume gives the ratio, which indicates how much membrane area is available per unit of volume.