97.0k views
5 votes
how many cubic blocks with a side length of 1/8 inch are needed to fill a rectangular prism with a length width and height of 3/4 inch 1/2 inch and 1/2 inch

User Keebus
by
7.4k points

1 Answer

4 votes
First lets calculate the total volume of the rectangular prism:
volume = length*width*height
v = (3/4)(1/2)(1/2) = (3*1*1)/(4*2*2) = 3/16
so the total volume of the prism is 3/16 cubic inches, now we need to know how many cubic blocks of 1/8 inch side length fill the 3/16 volume, that is solved by finding a number that multiplied by the volume of a cubic block of side 1/8 gives us 3/16, lets call the number x and write the respective equation:
the volume of the cubic block is (1/8)(1/8)(1/8) = 1/(8*8*8) = 1/512, therefore:
(1/512)x = 3/16
solving for x:
x = (3/16)*512 = 3*512/16
x = 96
so you need 96 cubic blocks of 1/8 inch sides to fill the stated prism
User Bayrinat
by
7.9k 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