Question

what is the lenght height and width of a rectanguar prism if they are in a ratio of 6:4:3 and the volume is 810

Answer 1

what is 6*4*3?

Answer 2

or rather; 6n * 4n * 3n = 810

Answer 3

no its like the ratio, its 6:4:3

Answer 4

so I need to find the measurments of each side by using those ratios

Answer 5

the sides l:h:w have a ratio of 6:4:3

volume of a prism is defined as l*h*w = 810

the only difference between the actual lengths, and the ratio, are some constant scaled factor.

Answer 6

therefore, we know:

length = 6n
height = 4n
width = 3n

and 6n*4n*3n = 810

solve for n

Answer 7

ohh thank you but I made a mistake, the surface area is 810 and I need to find the volume of the rectangular prism

Answer 8

...... same concepts, different "formula" tho

can you recall a good formula for surface area?

Answer 9

6n*4n*3n = Volume is still fine, and still have to determine the n value

Answer 10

2ab+2bc+2ac right?

Answer 11

sounds about right, but lets use lhw instead of abc

Answer 12

so my equation would be 6n*4n*3n= 2lw+2wh+2hl ?

Answer 13

2hl + 2hw + 2lw = 810

no, one formula is for surface area, and one is for volume. they will not generally equate to the same value

Answer 14

lhw
643

2lw+2wh+2hl = 810

2(6n)(3n)+2(3n)(4n)+2(4n)(6n) = 810

Answer 15

2(6n)(3n)+2(3n)(4n)+2(4n)(6n) = 810

36n^2 + 24n^2 + 48n^2 = 810

108n^2 = 810

n^2 = 810/108

Answer 16

ohhhhh wait why would you square the numbers?

Answer 17

so what does n represent?

Answer 18

btw thank you so much for helping!!

Answer 19

n represents the number that is scaling the ratio of 6:4:3 to its proper lengths

Answer 20

so after I find n what do I do?

Answer 21

i thought i covered that

Answer 22

length is equal to 6n
height is equal to 4n
width is equal to 3n

Answer 23

once you find n, you know that actual measurements and not just their ratio

Answer 24

ooohhhh I get it wait so n would be 7.5?

Answer 25

dunno, i aint got me calculator to find the sqrt of (810/108) but ill trust you on it

Answer 26

wait why would you find the square root?

Answer 27

you plug in the values for length width and height into the surface area formula and solve for n

2(6n)(3n)+2(3n)(4n)+2(4n)(6n) = 810

36n^2 + 24n^2 + 48n^2 = 810

108n^2 = 810

n^2 = 810/108

Answer 28

wait is it possible to do a square root of a decimal?

Answer 29

its possible to do the sqrt of any real number. it all depends on what you define as an acceptable output

Answer 30

ohhh so I got 2.738612788 so would I just round it to the nearest tenth?

Answer 31

rounding introduces a small error, the longer the decimal the smaller the error. so its up to you how far you want to take this in the end. my thought was to have 4 decies

Answer 32

does the solution ask for an approxiamte, or an exact value?

Answer 33

yeah it asks for an exact volume

Answer 34

then do not round to anything :)

Answer 35

you can simplify to:\[n=\sqrt{\frac{15}{2}}\]