(a)
To find:The ratios of heights of two similar prisms.
(a)
Answer to Problem 6ST2
The ratios of heights of two similar prismis
Explanation of Solution
Given information:
The base areas of two similar prism are
Calculation:
Let, the two base areas be
Expression of given two base areas of similar prism in ratio is:
To find the ratio of base areas, divide the numerator and denominator of the above expression by
Therefore, the base areas ratio of two similar prism in reduced form is
The theorem of similar solids states that if the scale factor of two similar solids is
Expression to determine height of prism from the above theorem is:
Substitute
To find the ratio of heights, apply square root at both sides in the above expression.
Therefore, the ratios of heights of two similar prism is
(b).
To find:The ratios of volumes of two similar prisms.
(b).
Answer to Problem 6ST2
The ratios of volumes of two similar prism is
Explanation of Solution
Given information:
The base areas of two similar prism are
Calculation:
As calculated in part (a), the value for
The theorem of similar solids states that if the scale factor of two similar solids is
Expression to determine the ratio ofvolumes of prismusing the above theorem is:
Substitute
Therefore, the ratio of volumes of two similar prismsis
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