Explain whether a cubic cell with side length x or a spherical cell with diameter x can exchange material with its environment faster.
Spherical cell with diameter x can exchange material with its environment faster.
Given:
Cubic cell of side length x and spherical cell with diameter x .
Calculation:
Surface area of cube is given by
Volume of cube is given by
Hence, surface area to volume ratio of cube is given by
Now, surface area of spherical cube is given by
Volume of spherical cube is given by
Therefore, surface area to volume ratio of spherical cell is given by
Since, surface area to volume ratio of spherical cell is higher than that of cubical cell.
Hence, a spherical cell with diameter x can exchange material with its environment faster.
Chapter 2 Solutions
Holt Mcdougal Larson Algebra 2: Student Edition 2012
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