Bacteria vary somewhat in size, but a diameter of 1.5 μ m is not unusual. a. What would be the volume (in cubic centimeters) of such a bacterium, assuming that it is spherical? Express your answer using two significant figures.
b. What would be the surface area (in square millimeters) of such a bacterium, assuming that it is spherical? Express your answer using two significant figures.

a) 1.8 × 10^-12 cm³ or 1.8 × 10^-12 cubic meters

b) 7.1 × 10^-6 mm² or 7.1 × 10^-6 square millimeters

Step-by-step explanation:

a) We are assuming that the shape of the bacteria is a sphere.

Hence, Volume of the Sphere(Bacteria) = 4/3 × π × r³

Diameter = 1.5 μm

Radius = Diameter/2 = 1.5μm/2

= 0.75μm

We are told that the volume should be in cubic centimeters

Converting 0.75μm to centimeters

1 μm = 1 × 10^-4 cm

0.75 μm =

Cross Multiply

= 0.75 μm × 1 × 10^-4 cm/ 1 μm

= 0.000075cm

Volume of the Sphere(Bacteria) = 4/3 × π × r³

= 4/3 × π × (0.000075)³

= 1.767145867 × 10^-12 cm³

Approximately as 2 significant figures = 1.8 × 10^-12 cm³

b) The formula for the Surface area of a Sphere = 4πr²

Diameter = 1.5 μm

Radius = Diameter/2 = 1.5μm/2

= 0.75μm

We are told that the surface area should be in square millimeters

Converting 0.75μm to millimeters

1 μm = 0.001 mm

0.75 μm =

Cross Multiply

= 0.75 μm ×0.001mm/ 1 μm

= 0.00075mm

Surface Area of a Sphere

= 4 × π × r²

= 4 × π × 0.00075²

= 7.06858 ×10^-6 mm²

Approximately to 2 significant figures

= 7.1 × 10^-6 mm²

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