Question

A farm grain bin, which is in the shape of a cylinder, has a radius of 20 ft and a height of 50 ft. If the height and radius are increased by x ft, find the polynomial that gives the volume of the new grain bin in ft.

a) (V = π(20 + x)²(50 + x))
b) (V = π(20 - x)²(50 - x))
c) (V = π(20x)²(50x))
d) (V = π(20 + x)(50 + x))

Answer 1

The polynomial that represents the volume of the new grain bin after increasing the radius and height by 'x' feet is V = π(20 + x)²(50 + x).

Step-by-step explanation:

To find the polynomial that gives the volume of the new grain bin after increasing both the height and radius by x feet, we use the formula for the volume of a cylinder: V = πr²h. If the radius is initially 20 ft and the height is 50 ft, after the increase, the new radius is (20 + x) and the new height is (50 + x). Therefore, the volume of the new grain bin would be given by the polynomial V = π(20 + x)²(50 + x), which corresponds to option a).