The volume of a cylinder varies jointly as its altitude and the square of the radius of its base. If the volume of a cylinder is 2,199 cubic centimeters when the radius of the base is 10 centimeters and its altitude is 7 centimeters, find the volume of a cylinder that has a base of radius 70 centimeters. The altitude of the cylinder is 56 centimeters. A)V = 861,952 cm ³ B)V = 862,023 cm ³ C)V = 861,979 cm ³ D)V = 862,008 cm ³ E)V = 862,118 cm ³

Question

Quizplus · Accepted Answer

The volume V of a cylinder is given by V = k * r^2 * h, where k is a constant, r is the radius, and h is the altitude. First, find k using the given values: 2199 = k * 10^2 * 7, so k = 3.14142857. Then, use this k to find the new volume: V = 3.14142857 * 70^2 * 56 = 862,008 cm³.

The Volume of a Cylinder Varies Jointly as Its Altitude