Question

the total recommended area A, in square feet, of a sailboat's sails is given by [{MathJax fullWidth='false' A = 16\sqrt[3]{d^2} }] where d is the displacement of the hull in cubic feet. If a sailboat has 400 ft² of sail, what is the displacement of the hull of the sailboat?

Answer 1

125ft³

Explanation

Given the area of the sail boat expressed as
`A = 16\sqrt[3]{d^2}`. IF the area is 400ft², we are to find the displacement d;

Substitute A = 400 into the expression given and find d as shown;

`A = 16\sqrt[3]{d^2}\\400 = 16\sqrt[3]{d^2}\\400/16 = \sqrt[3]{d^2}\\cube \ both \ sides\\(400/16)^3=( \sqrt[3]{d^2})^3\\64,000,000/4096 = d^2\\d = √(64,000,000/4096) \\d = 8,000/64\\d = 125 ft^3`

Hence the displacement of the hull of the sailboat is 125ft³