Question

N a water treatment plant, water passes through a cone-shaped filter with a height of 4 m and a diameter of 9 m. The water flows from the filter into a cylinder below it. One full cone-shaped filter fills one-fifth of the cylinder.
What are the dimensions of the cylinder? Use 3.14 to approximate pi.
A. h = 3 m; r = 3 m
B.h = 4.23 m; r = 5 m
C.h = 15 m; r = 6 m
D.h = 33.75 m; r = 2 m

Answer 1

Given:
Cone-shaped filter: height = 4m ; diameter = 9m
cylinder:  one full cone-shape filter fills 1/5 of the cylinder

volume of the cone  = π r² h/3 = 3.14 * (4.5m)² * 4m/3
V = 3.14 * 20.25m² * 1.33m
V = 84.57 m³

84.57 m³ ÷ 1/5 = 84.57 m³ * 5 = 422.85 m³ volume of the cylinder

Volume of cylinder = π r² h

Choice A: V = 3.14 * (3m)² * 3m = 3.14 * 9m² * 3m = 84.78 m³
Choice B: V = 3.14 * (5m)² * 4.23m = 3.14 * 25m² * 4.23m = 332.10 m³
Choice C: V = 3.14 * (6m)² * 15m = 3.14 * 36m² * 15m = 1695.60 m³
Choice D: V = 3.14 * (2m)² * 33.75 m = 3.14 * 4m² * 33.75m = 423.90 m³

The closest answer is Choice D. height = 33.75 m ; radius = 2 m