Question

A cylindrical hole is drilled into a piece of wood. The radius of the hole is 8 millimeters less than the height, x, of the hole. If 1,024π cubic millimeters of material was removed to make the hole, the equation x3 + x2 + x − 1,024 = 0 can be used to find that the height of the hole is millimeters.

Answer 1

Using the solver function of the calculator, we can find the roots of the polynomial.

x1 = 9.72484

x2 = −5.36242+8.74882i

x3 = −5.36242−8.74882i

  Since dimension cannot be imaginary, therefore the height of the cylindrical hole is 9.72 mm. Calculating for radius r: r = 9.72 mm – 8 mm r = 1.72 mm   The volume of cylinder is given as: V = π r^2 h V = π (1.72)^2 (9.72) V = 90.34 mm^3