A pentagonal prism has dimensions that are four times the dimensions of a similar pentagonal prism. So its volume is (8, 16, 64,
2 answers:
Answer: The volume of the bigger pentagonal prism will be 64 times the volume of the smaller pentagonal prism.
Step-by-step explanation: Given that a pentagonal prism has dimensions that are four times the dimensions of a similar pentagonal prism.
We know that
the volume of a pentagonal prism with base edge a units and height h units is given by
If a' and h' are the base edge and height of the similar pentagonal prism, then according to the given information, we have
So, the volume of the similar bigger prism will be
Thus, the volume of the bigger pentagonal prism will be 64 times the volume of the smaller pentagonal prism.
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Answer:
p = 4
Step-by-step explanation:
The usually recommended procedure for solving a proportion is to "cross multiply", then divide by the coefficient of the variable. (Solve the remaining one-step equation.)
<h3>Cross multiply</h3>This means multiply both sides of the equation by the product of the denominators:
(15/6)(6p) = (10/p)(6p) . . . . "cross multiply"
15p = 60 . . . . . . simplify
<h3>Second step</h3>Now, divide by the coefficient of the variable.
15p/15 = 60/15
p = 4
The solution is p = 4.
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<em>Additional comment</em>
If the variable is in the <em>numerator</em> of the proportion, using cross multiplication, you will find that you end up multiplying and dividing by the other denominator. To solve it in that case, you only need to multiply by the denominator under the variable.
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For example, to solve ...
2/5 = p/10
you only need to multiply by 10. You don't need to multiply by 50, then divide by 5.
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Any proportion can be written 4 ways:
This suggests another strategy: invert the whole proportion, then solve it as one with p in the numerator:
6/15 = p/10 ⇒ p = 10(6/15) = 4