67.4k views
2 votes
Find the missing dimension of the prism. Round your answer to the nearest hundredth.

Volume = 72.66 in.?

Х

2 in.

User Karthik G
by
7.6k points

1 Answer

4 votes

Answer:


x = 6.99in

Explanation:

Given


l =2in


Volume = 72.66in^3

See attachment for prism

Required

Find x

The prism has a regular hexagon base

The base area is calculated as:


Base\ Area= (3\sqrt 3)/(2)l^2

This gives:


Base\ Area= (3\sqrt 3)/(2) * 2^2


Base\ Area= (3\sqrt 3)/(2) * 4


Base\ Area= 3\sqrt 3 * 2


Base\ Area= 6\sqrt 3

Side x represents the height.

So, we have:


Volume = Base\ Area*x

Make x the subject


x = (Volume )/( Base\ Area)


x = (72.66in^3)/(6\sqrt 3 in^2)


x = (72.66)/(6\sqrt 3)in


x = (12.11)/(\sqrt 3)in


x = 6.99in --- approximated

Find the missing dimension of the prism. Round your answer to the nearest hundredth-example-1
User Ankanna
by
7.8k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories