A regular pentagonal prism has 9-cm base edges. A larger,

nuais6lfp

nuais6lfp

Answered question

2021-11-23

A regular pentagonal prism has 9-cm base edges. A larger, similar prism of the same material has 36-cm base edges. How does each indicated measurement for the larger prism compare to the same measurement for the smaller prism? a. the volume b. the weight.

Answer & Explanation

Dona Hall

Dona Hall

Beginner2021-11-24Added 15 answers

Step 1
(a)
If the scale factor of two similar solids is ab or a:b, then:
1) the ratio of their corresponding areas is a2b2ora2:b2 , and
2) the ratio of their volumes is a3b3 or a3:b3.
Using the corresponding dimensions, the scale factor is ab=369=41 or 4:1.
So, the ratio of the volumes is:
a3b3=4313=641 or 64:1
This means that the volume of the larger prism is 64 times the volume of the smaller prism.

Poul1963

Poul1963

Beginner2021-11-25Added 15 answers

Step 2
(b)
The capacities and weights of similar objects made of the same material are proportional to their volumes.
So, the ratio of the weights is also 64:1. This means that the weight of the larger prism is 64 times the weight of the smaller prism.

Do you have a similar question?

Recalculate according to your conditions!

Ask your question.
Get an expert answer.

Let our experts help you. Answer in as fast as 15 minutes.

Didn't find what you were looking for?