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The surface area of a sphere is given by the expression, . The volume of the sphere is given by the expression, . Dividing the surface area expression by the volume expression, we get, . So the ratio is inversely dependent on the value of r. Given for the sphere, the surface area = 588 m², and the volume = 1372 m³.

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The volume enclosed by a sphere is given by the formula Where r is the radius of the sphere. In the figure above, drag the orange dot to change the radius of the sphere and note how the formula is used to calculate the volume.

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In biology, the surface-area-to-volume quotient Q of a single spherical cell is given by the formula Q= 3/r where r is the radius of the cell. Suppose you need to calculate diameter of the cells given the surface area to volume quotients of the cells.

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This is because single-celled creatures have a very high surface-area-to-volume ratio, so have lots of available surface to exchange substances. Multi-celled creatures on the other hand tend to have a low surface-area-to-volume ratio , meaning their outer surfaces cannot exchange substances fast enough for all their cells.

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For example, use the formulas V = s3 and A = 6 s2 to find the volume and surface area of a cube with sides of length s = 1/2.

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Background Knowledge: The surface area to volume ratio of an object is determined by dividing the surface area by the volume and putting Read More How Does the Surface Area to Volume Ratio Affect Heat Loss in Organisms?