The volume of a right circular cylinder varies jointly as the height and the square of radius of the base. Suppose a right circular cylinder has the measurements V=58096.28 cubic yards, r=29 yards and h=22 yards. Step 1 of 2 : Find the constant of proportionality k, rounded to two decimal places if necessary, and use it to write an equation that models the relationship.

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Question
The volume of a right circular cylinder varies jointly as the height and the square of radius of the base. Suppose a right circular cylinder has the measurements V=58096.28 cubic yards, r=29 yards and h=22 yards. Step 1 of 2 : Find the constant of proportionality k, rounded to two decimal places if necessary, and use it to write an equation that models the relationship.
Expert Solution
Step 1

Given that: 

Volume(V)=58096.28 cubic yards,r=29yards,h=22yardsand the right circular cylinder.

A right circular cylinder is defined as a cylinder that has a closed surface having two parallel bases on both ends and their element are perpendicular to their base.

The volume of the cylinder is,

V=kr2h

where r-radius and h-height and V-Volume.

To find the value of k:

Put the value of r,h, and V in the volume of the cylinder formula and we get the proportionality constant k.

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