1. What would be the volume (in cubic centimeters) of such a bacterium, assuming that it is spherical?
2. What would be the surface area (in square millimeters) of such a bacterium, assuming that it is spherical?
3 Answers
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r = 0.65 μm = 6.5×10⁻⁵ cm = 6.5×10⁻⁴ mm
volume = (4/3)πr³
= (4/3)π(6.5×10⁻⁵)³
≅ 1.15×10⁻¹² cm³
surface area = 4πr²
= 4π(6.5×10⁻⁴)²
≅ 5.3×10⁻⁶ mm²
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Sphere V = ⁴/₃πr³
A = 4πr²
V = ⁴/₃π(1.3e-6)³ = 9.20e-18 m³
9.20e-18 m³ x (100 cm/m)³ = 9.20e-12 cm³
A = 4π(1.3e-6)² = 2.12e-11 m²
2.12e-11 m² x (1000 mm/m)² 2.12e-5 mm²
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1.3 um = 0.00013 cm = 0.0013 mm
V = (4/3) pi r^3
r = 0.000065 cm
V = 1.15 x 10^-12 cm^3
SA = 4 pi r^2
r = 0.00065 mm
SA = 5.31 x 10^-6 mm^2