Question

The width of a box is two-thirds of it's length and height is one-third of it's length. If the volume of the box is 48m³, find the are of the base of the box.

Please teach it step by step ​

Answer 1

Explanation:

`V=48,w=(2)/(3) l,h=(1)/(3) l,l=l`

`V=whl`

`48=(2)/(3) l* (1)/(3) l * l`

`48=(2)/(9) l^3`

`l^3=216`

`l=\sqrt[3]{216}`

`l=6`

So length = 6m, width = 4m, height = 2m

Area of base = length x width = 24
`m^2`

Answer 2

We know that the width is two-thirds of the length, so we can replace "width" with "2/3 length":

Volume = length x (2/3 length) x (1/3 length)

We also know that the height is one-third of the length, so we can replace "height" with "1/3 length": Volume = length x (2/3 length) x (1/3 length) = 48m³

Now we can simplify this equation by multiplying the lengths together:

(2/3 length) x (1/3 length) = 2/9 length² So the equation becomes: Volume = length x (2/9 length²) = 48m³

We can solve for the length by dividing both sides by (2/9 length²):

length = 3∛144 = 6m

Now that we know the length of the box is 6m, we can find the width and height: width = 2/3 length = 4m

height = 1/3 length = 2m

Finally, we can find the area of the base of the box by multiplying the length and width:

Area of base = length x width = 6m x 4m = 24m²


* Therefore, the area of the base of the box is 24m²