# Biology

Compared with a smaller cell, a larger cell of the same shape has

a. the same surface-to-volume ratio.
b. a smaller cytoplasm-to-nucleus ratio.
c. less surface area.
d. a smaller average distance between its mitochondria and the nucleus.
e. less surface area per unit of volume.

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1. Assume the cell is a sphere. The volume inside a sphere is given by the formula

V = 4/3 pi r^3

where r is the radius of the sphere. This formula was first derived by Archimedes, who showed that the volume of a sphere is two-thirds that of a circumscribed cylinder. (This assertion follows from Cavalieri's principle.) In modern mathematics, this formula is most easily derived using integral calculus, e.g. using disk integration.
The surface area of a sphere is given by the formula

A = 4 pi r^2

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2. If im understanding your explanation properly, the correct answer is e??

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3. Yup!

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