How many rectangular prisms can you make with 18 cubes
Asked by maham237 @ in Mathematics viewed by 344 People
Quentin has 18 unit cubes. How many different rectangular prisms can he build if he uses all of the cubes?
Answered by maham237 @
18 unit cubes means that the area of the rectangular prisms (cuboids), will be 18 cm^3
We need to work out the three factors that can be multiplied to get 18. Let's start simple and give the cuboid a height of one. That means we need to work out heights and lengths that are factors of 18. Factors of 18 are:
1*18
2*9
3*6
So there we have three cuboids, of dimensions 1*1*18, 1*2*9, and 1*3*6
Now things get more complicated. We need to use the other factors of 18 as heights. Let's start with a height of 2. This means that the height and length of the rectangle need to be factors of 9, because 18/2 = 9.
Factors of 9 are:
1*9
3*3
So that gives us two cuboids, of dimensions 2*1*9 and 2*3*3
Use the next factor, which is 3. 18/3 = 6, so the height and length have to be factors of 6. Factors of 6 are:
1*6
2*3
So that gives us two cuboids, of dimensions 3*1*6 and 3*2*3
At this point, we don't need to go through any more factors, because they will all certainly end up with the same dimensions as the previous ones we've found
Our final cuboids are 1*1*18, 1*2*9, 1*3*6, 2*1*9, 2*3*3, 3*1*6, 3*2*3
Now we need to eliminate all the duplicates.
1*2*9 = 2*1*9
1*3*6 = 3*1*6
2*3*3 = 3*2*3
So we'll just get rid of all the ones on the right hand side, because they're equivalents of the ones on the left
So we end up with cuboids of dimensions 1*1*18, 1*2*9, 1*3*6, 2*3*3
Hope that helps, I know some of that may be confusing, you can comment/pm and I'll try to explain it more :)
Similar Questions
How many edges does a rectangular prism have
Asked by maham237 @ in Mathematics viewed by 361 persons
How many edges does a rectangular prism have?
6
8
10
12
How many vertices in a rectangular prism
Asked by maham237 @ in Geography viewed by 297 persons
How many vertices does a rectangular prism have?
How many cubes would you use to make the structure below
Asked by maham237 @ in Mathematics viewed by 386 persons
How many cuboids are needed to make a cube
Asked by admin @ in Math viewed by 351 persons
How many cuboids are need to make a cube if dimensions of cuboid is 5×2×5 cm^3?
Carmen enters a painting in an art contest. the contest rules say that all paintings must be rectangular, with an area no greater than 3,003.04cm. carmen's painting is 16 cm wide. what is the greatest length the painting can have and still have an area within the contest rules.
Asked by maham237 @ in Mathematics viewed by 317 persons
Find the inverse of the function. f(x) = the cube root of quantity x divided by seven. - 9
Asked by maham237 @ in Mathematics viewed by 301 persons
Sarah is making a scale drawing of a painting that is 48 in wide by 120 in high
Asked by maham237 @ in Mathematics viewed by 1068 persons
Sarah is making a scale drawing of a painting that is 48 in. wide by 120 in. high. Her paper is 12 in. wide and 24 in. tall. She decides …
If it takes 42 minutes to load 3 1/2 trucks, how many minutes will it take to load 6 1/2 trucks?
Asked by maham237 @ in Physics viewed by 384 persons
A running mountain lion can make a leap 10.0 m long, reaching a maximum height of 3.0 m.
Asked by wiki @ in Physics viewed by 656 persons
A running mountain lion can make a leap 10.0 m long, reaching a maximum height of 3.0 m.?
a.What is the speed of the mountain lion just as it leaves …
One base of an octagonal prism has an area of 235 in.² the surface area of the prism is 500 in.² what is the area of the sides of the prism?
Asked by amit7180 @ in Math viewed by 417 persons
How many edges and vertices does a triangular prism have
Asked by admin @ in Mathematics viewed by 320 persons
How many vertices does a triangular prism have? 4 5 6 9
How to find the volume of a right rectangular prism
Asked by admin @ in Mathematics viewed by 309 persons
Find the volume of this right rectangular
prism.
3 ft
15 ft
10 ft
[? ]ft?
How many yards of ribbon to make a cheer bow
Asked by admin @ in Mathematics viewed by 381 persons
To make cheer hair bows out of ribbon, Rachel needs 2 ¼ feet of ribbon. If Rachel bought 13 ½ yards of ribbon at a sale, how many hair bows …
How many vertices and edges does a triangular prism have
Asked by admin @ in Mathematics viewed by 332 persons
How many vertices does a triangular prism have? 4 5 6 9
How many types of rocks make up the earth's crust
Asked by admin @ in Physics viewed by 333 persons
How many types of rocks make up the Earth's crust?
Most viewed questions in Mathematics
Unit 6 similar triangles homework 2 similar figures answer key
Asked by maham237 @ in Mathematics viewed by 18335 persons
All things algebra unit 7 polygons and quadrilaterals answer key
Asked by admin @ in Mathematics viewed by 8132 persons
Gina wilson all things algebra 2016 answer key unit 11
Asked by admin @ in Mathematics viewed by 5760 persons
Unit 1 geometry basics homework 4 angle addition postulate answers
Asked by maham237 @ in Mathematics viewed by 3925 persons
Unit 6 exponents and exponential functions homework 8 answer key
Asked by maham237 @ in Mathematics viewed by 3240 persons
The manager of a vacation resort believes that the ages
Asked by maham237 @ in Mathematics viewed by 2914 persons
What is 271 403 rounded to the nearest ten thousand
Asked by maham237 @ in Mathematics viewed by 2778 persons
Unit 1 geometry basics homework 3 angle relationships answer key
Asked by maham237 @ in Mathematics viewed by 2571 persons
Why would a prism beat a sphere in a competition?
Asked by maham237 @ in Mathematics viewed by 2472 persons
An artist sells a painting for 20.50 but uses 5.75
Asked by maham237 @ in Mathematics viewed by 2420 persons
Unit 4 congruent triangles homework 1 classifying triangles answer key
Asked by maham237 @ in Mathematics viewed by 2412 persons
Unit 4 congruent triangles homework 2 angles of triangles
Asked by maham237 @ in Mathematics viewed by 2068 persons
Compare the values of the 2s and 5s in 55220
Asked by maham237 @ in Mathematics viewed by 1786 persons