Question

The width of a block of wood with rectangular cross-section is x cm . it's height is two - thirds its width and it's length is 4 times its height. What is its volume in cm3​

Answer 1

The volume (V) of a rectangular block of wood can be found by multiplying its length, width, and height:

V = lwh

From the problem, we know that the height (h) is two-thirds of the width (x), or h = (2/3)x. We also know that the length (l) is 4 times the height, or l = 4h. Substituting these values into the formula for volume, we get:

V = lwh = (4h)(x)(h) = 4xh^2

Substituting h = (2/3)x, we get:

V = 4x((2/3)x)^2 = 4x(4/9)x^2 = (16/9)x^3

Therefore, the volume of the block of wood is (16/9)x^3 cubic centimeters.