Question

the dimensions of a rectangular solid are in the ratio of 1:6:6 and its volume is 562.5 cm^3 , find the measurement of the edges?

Answer 1

cozy has the right idea, but volume is found by multiplying the 3 dimensions

The 1:6:6 ratio means that the lengths are 1x , 6x and 6x
the volume will be 36x^3= 562.5 cc
solve for x

Answer 2

the 1:6:6 is the length the width and the height's ratio
and the 562.5 is the volume so if you multiply the all the outcome of the ratio you should come up with 562.5

Answer 3

i come up with 15.625 but if i multiply it i wont give the volume that is given

Answer 4

you found x^3

x^3= 5652.5/36 = 15.625

Answer 5

do i need to cube root it?

Answer 6

A calculator gives the answer, but if you write it as an improper fraction
\[ x^3 = \frac{125}{8} \]

Answer 7

yay thank you hahaha all i forgot is to cube root it

Answer 8

to solve, raise both sides to the 1/3 power (that means cube root)
\[ \left(x^3\right)^{\frac{1}{3}} = \left(\frac{125}{8}\right)^{\frac{1}{3}}\]
\[ x= \frac{125^{\frac{1}{3}}}{8^{\frac{1}{3}}} \]

Answer 9

the x in 2.5

Answer 10

thank you a lot

Answer 11

and to finish the question
the measurement of the edges are 2.5, 15 and 15

Answer 12

yeah i found the answer already ty