The surface area, S, and volume, V, of a right circular...

The surface area, $S$, and volume, $V$, of a right circular cylinder of radius, $r$, and height, $h$, are given by the formulas a) Determine the surface area of the cylinder if its height is 10 inches and its volume is 160 cubic inches. b) Determine the radius if the height is 10 inches and the volume is 160 cubic inches. c) Determine the radius if the height is 10 inches and the surface area is 160 square inches.

The surface area, $S$, and volume, $V$, of a right circular cylinder of radius, $r$, and height, $h$, are given by the formulas
a) Determine the surface area of the cylinder if its height is 10 inches and its volume is 160 cubic inches.
b) Determine the radius if the height is 10 inches and the volume is 160 cubic inches.
c) Determine the radius if the height is 10 inches and the surface area is 160 square inches.

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Key Concepts

Algebraic Manipulation and Equation Solving

Algebraic manipulation involves rearranging and combining equations to isolate variables of interest. In the context of this problem, it includes setting up equations using the volume and surface area formulas and potentially solving quadratic equations to find unknown dimensions such as the radius or height.

Surface Area of a Cylinder

The surface area of a cylinder includes the areas of the two circular bases and the lateral surface area of the curved side. The formula S = 2? r² + 2? r h captures this by summing the areas of the bases and the side, and it is used when solving problems involving material coverage or paint required for the surface.

Right Circular Cylinder

A right circular cylinder is a three-dimensional shape with two identical circular bases connected by a curved surface at a perpendicular angle to the bases. Understanding its properties is fundamental in geometry and helps in solving problems related to its dimensions such as radius, height, volume, and surface area.

Volume of a Cylinder

The volume of a cylinder is calculated by multiplying the area of its circular base by its height. The formula V = ? r² h encapsulates this concept, and it is used to determine one of the dimensions when the volume and another variable (either r or h) are known.

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