If y varies directly as the cube of x, and y=
54 when x = 3, find y when x= 5.

250

Step-by-step explanation:

From the question given above,

y varies directly as the cube of x. This can be written as

y ∝ x³

y = Kx³

Next, we shall determine the value of the constant (K) as follow:

y = 54

x = 3

K =?

y = Kx³

54 = K × 3³

54 = K × 27

Divide both side by 27

K = 54/72

K = 2

Finally, we shall determine the value of y when x is 5. This can be obtained as follow:

x = 5

K = 2

y =?

y = Kx³

y = 2 × 5³

y = 2 × 125

y = 250

Therefore, the value of y is 250