Question

The weight Wkg of a metal bar varies jointly

as its length L metres and the square of its
diameter d mm. If W= 140 when d =4 and L= 54, find d in terms of W and L. ​

Answer 1

d =
`\sqrt{(216W)/(35L) }`

Explanation:

Given that W varies jointly as L and d² then the equation relating them is

W = kLd² ← k is the constant of variation

To find k use the condition W = 140 when d = 4 and L = 54, thus

140 = k × 54 × 4² = 864k ( divide both sides by 864 )

`(140)/(864)` = k , that is

k =
`(35)/(216)`

W =
`(35)/(216)` Ld² ← equation of variation

Multiply both sides by 216

216W = 35Ld² ( divide both sides by 35L )

`(216W)/(35L)` = d² ( take the square root of both sides )

d =
`\sqrt{(216W)/(35L) }`