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To find: The ratio of the volume of the larger tree to that of the smaller tree.
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Answer to Problem 30E
The ratio of the volume of the larger tree to that of the smaller tree is 1.069.
Explanation of Solution
Given information:
The height of the first tree is
Formula used:
The volume of a cylinder is
The volume of a sphere is
Calculation:
The height of the first tree is
The height of the second tree is
The radius of both trees is
The volume of a cylinder is
Where,
The volume of a sphere is
Where
The 90% of the height of the first tree is a cylindrical trunk. Therefore,
Hence, the volume
Since 10% of the height of the tree is a spherical blob, we get
Therefore, the radius of the sphere is as follows
So, the volume of the spherical blob part of the first tree is shown below
Therefore, the volume of the first tree is
Since half of the height of the tree is a cylindrical trunk, we find that
The volume of cylindrical part of the second tree is shown below
Since half of the height of the tree is spherical blob, So
Therefore the radius of sphere can be calculate as
The volume of the second tree with half of the height in the spherical blob is
The volume of the second tree is
Since
The ratio is
Hence, the ratio
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Chapter 1 Solutions
Modeling the Dynamics of Life: Calculus and Probability for Life Scientists
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