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If this cell has a diameter of 10um, calculate the total surface area of the neuron and the volume of the neuron. Express the units in cm².

User Nafissatou
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Final answer:

To calculate the surface area of a neuron, we can use the formula for the surface area of a sphere. The surface area of the neuron is 100πμm², or π*10^-6 cm².

Step-by-step explanation:

To calculate the surface area of a neuron, we can use the formula for the surface area of a sphere, which is 4πr^2, where r is the radius of the sphere.

In this case, the diameter of the cell is given as 10μm, so the radius is half of that, which is 5μm. Plugging this value into the formula, we get:

Surface area = 4π(5μm)^2 = 4π(25μm^2) = 100πμm^2

To convert this to cm², we can use the conversion factor 1μm^2 = 10^-8 cm²:

Surface area = 100πμm^2 * (10^-8 cm²/μm^2) = π*10^-6 cm²

To calculate the volume of the neuron, we can use the formula for the volume of a sphere, which is (4/3)πr^3:

Volume = (4/3)π(5μm)^3 = (4/3)π(125μm^3) = (500/3)πμm^3

To convert this to cm³, we can use the conversion factor 1μm^3 = 10^-12 cm³:

Volume = (500/3)πμm^3 * (10^-12 cm³/μm³) = (5/3)π*10^-9 cm³

User StrawHara
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