Solve the variation problems in Exercises 93

Name: Problem 98, Chapter 3: Precalculus
Uploaded: 2021-06-19T13:44:08-08:00
Duration: 1 min 49 s
Channel: Barsha Rana
Description: Solve the variation problems in Exercises 93–98. The volume of a pyramid varies jointly as its height and the area of its base. A pyramid with a height of 15 feet and a base with an area of 35 square feet has a volume of 175 cubic feet. Find the volume of a pyramid with a height of 20 feet and a base with an area of 120 square feet.

Solve the variation problems in Exercises 93–98. The volume of a pyramid varies jointly as its height and the area of its base. A pyramid with a height of 15 feet and a base with an area of 35 square feet has a volume of 175 cubic feet. Find the volume of a pyramid with a height of 20 feet and a base with an area of 120 square feet.

Solve the variation problems in Exercises 93–98.
The volume of a pyramid varies jointly as its height and the area of its base. A pyramid with a height of 15 feet and a base with an area of 35 square feet has a volume of 175 cubic feet. Find the volume of a pyramid with a height of 20 feet and a base with an area of 120 square feet.

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Key Concepts

Joint Variation

Joint variation describes situations where a quantity varies directly as the product of two or more other quantities. This principle means that if any one of the factors increases, the quantity in question increases proportionally, and if any of the factors decreases, the quantity decreases accordingly, provided the constant of proportionality remains unchanged.

Constant of Proportionality

The constant of proportionality is the fixed multiplier that connects the dependent variable to the product of the independent variables in a variation problem. It allows the relationship to be quantified and used to compute unknown values once the relationship is established.

Algebraic Modeling of Variation

In solving variation problems, the relationship between the variables is expressed as an algebraic equation. This process typically involves determining the constant of proportionality using given data and then substituting any new known values into the model to find the unknown variable.

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