Answered: For figure, determine the volume of…

Structural Analysis

6th Edition

ISBN:9781337630931

Author:KASSIMALI, Aslam.

Publisher:KASSIMALI, Aslam.

Chapter2: Loads On Structures

Section: Chapter Questions

Problem 1P

See similar textbooks

Related questions

Concept explainers

Question

For figure, determine the volume of solid generated by the revolution of this area around a vertical axis passing through the left edge of the figure. Also determine the centroid of the generated solid.

A=218

B=41

C=11

Expert Solution

Step 1

Consider the given figure with the following changes:

The volume of solid generated by the revolution of this area around a vertical axis passing through the left edge is calculated as follows:

$Volume of the required figure = Volume of the right cylinder made by the rectangle LNRQ - Volume of sphere made by the quadrant LPQ - 1 / 2 times the volume of the hollow right cylinder made by the rectangle MNRO .$

Volume of the right cylinder made by the rectangle LNRQ $= π R^{2} h$

Substitute, R = A + C = 218 +11 = 229 and h = B = 41

Volume of the right cylinder made by the rectangle LNRQ $= 3.14285 \times {(229)}^{2} \times 41 = 6.754678 \times 10^{6} u n i t s^{3}$

Volume of sphere made by the quadrant LPQ $= \frac{2}{3} π r^{3}$

Substitute, r = B = 41

Volume of sphere made by the quadrant LPQ $= \frac{2}{3} \times 3.14285 \times 41^{3} = 1.44347 \times 10^{5} u n i t s^{3}$

1/2 times the volume of the hollow right cylinder made by the rectangle MNRO $= \frac{π (R^{2} - r^{2}) h}{2}$

Substitute, R = A + C = 218 +11 = 229, r = A = 218, and h = B = 41

1/2 times the volume of the hollow right cylinder made by the rectangle MNRO $= \frac{π (229^{2} - 218^{2}) 41}{2} = 3.16794 \times 10^{5} u n i t s^{3}$

Calculate the volume of the required figure as follows:

Volume of the required figure $= 6.754678 \times 10^{6} - 1.44347 \times 10^{5} - 3.16794 \times 10^{5}$

$= 6.293537 \times 10^{6} u n i t s^{3}$

Therefore, the volume of the solid generated by the revolution of this area around a vertical axis passing through the left edge is $= 6.293537 \times 10^{6} u n i t s^{3}$ .

Step by step

Solved in 2 steps with 2 images

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, civil-engineering and related others by exploring similar questions and additional content below.

Similar questions