Question

Brainliest please help! A storage bin is a rectangular prism. Its volume is 300 cm cubed.
The width of the prism is one-third its length.
its height is two-thirds its length.
Determine the dimensions of the bin.

Answer 1

Answer:

∛50 cm, 2∛50 cm, 3∛50 cm

Step-by-step explanation:

V= wlh

V=300 cm³

w= 1/3l

h= 2/3l

---------

• l*1/3l*2/3l=300
• 2/9l³=300
• l³= 1350
• l= ∛1350= 3∛50 cm
• w= 1/3*3∛50= ∛50 cm
• h= 2/3*3∛50= 2∛50 cm

Answer 2

Answer:

Length is 11.052cm

Width is 3.684cm

Height is 7.386cm

Step-by-step explanation:

Let length be x, width y and height Z

Width (y) = X/3 , height (z) = 2x /3

volume =xyz

volume = x(x/3)(2/3)x

Volume = (2/9)x³

But Volume =300

300= (2/9)x³

300/(2/9) = x³ (make x³ the subject to find x )

1350 = x³

x=3√(1350)

x=11.052cm

Length is 11.052cm

Width = x/3 =11.052 /3

= 3.684cm

Height = 2x/3 = 2(11.052) /3

= 7.368cm

You can check it by multiplying LWH to see if you get 300 (the volume)