OpenStudy (habbster):

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?

5 years ago
OpenStudy (phi):

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

5 years ago
OpenStudy (habbster):

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

5 years ago
OpenStudy (habbster):

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

5 years ago
OpenStudy (phi):

you found x^3 x^3= 5652.5/36 = 15.625

5 years ago
OpenStudy (habbster):

do i need to cube root it?

5 years ago
OpenStudy (phi):

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

5 years ago
OpenStudy (habbster):

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

5 years ago
OpenStudy (phi):

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

5 years ago
OpenStudy (habbster):

the x in 2.5

5 years ago
OpenStudy (habbster):

thank you a lot

5 years ago
OpenStudy (phi):

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

5 years ago
OpenStudy (habbster):