Question

Darnisha uses sheet metal to create a box. The polynomial function V (a) = 4x³-520x² +1,2002 gives the volume in cubic centimeters of the box in

terms of its height, z. If Darnisha creates a box with a volume of 72, 500 cm³, what is the height of the box rounded to the nearest tenth of a centimeter?

Answer 1

The height of the box rounded to the nearest tenth of a centimeter is 35.7 centimeters.

Darnisha has to find the value of z for V(z) = 72,500.

V (a) = 4x³-520x² +1,2002

=> 4z³-520z² +1,2002 = 72,500

=> z³-130z² + 3000.5 = 18125

Multiply both sides of the equation by 4

=> 4z³-520z² +12002 = 72,500

=> z³-130z² + 3000.5 = 18125

=> z³-130z² + 3000.5 - 18125 = 0

=> z³-130z² - 15124.5 = 0

Use a graphing calculator to solve z³-130z² - 15124.5 = 0

z ≈ 35.74

The height of the box rounded to the nearest tenth of a centimeter is 35.7 centimeters.

So the answer is 35.7