MHB Calculating Volume of a Solid by Subtracting Volumes of Basic Shapes

  • Thread starter Thread starter mathlearn
  • Start date Start date
  • Tags Tags
    Cylinder Volume
Click For Summary
The discussion focuses on calculating the volume of a solid by subtracting the volumes of a cylinder and a hemisphere. The user has already calculated the volumes using the formulas for each shape: the cylinder's volume is πa²h and the hemisphere's volume is (2/3)πa³. To find the volume of the solid, the volume of the hemisphere is subtracted from that of the cylinder. The final step involves plugging in the calculated volumes and simplifying the expression. This approach emphasizes the importance of showing progress when seeking help in problem-solving.
mathlearn
Messages
331
Reaction score
0
Please solve this problem

View attachment 5776

:)
 

Attachments

  • New Document 217-Page 2.jpg
    New Document 217-Page 2.jpg
    112.8 KB · Views: 141
Last edited by a moderator:
Mathematics news on Phys.org
mathlearn said:
Please solve this problem

:)

Good evening and welcome to MHB! :D

We ask that our users show their progress (work thus far or thoughts on how to begin) when posting questions. This way our helpers can see where you are stuck or may be going astray and will be able to post the best help possible without potentially making a suggestion which you have already tried, which would waste your time and that of the helper.

It is also MHB policy to not answer questions which are for credit or for exams.

Can you post what you have done so far?
 
Thank you super Sonic

So far

I calculated the volume of the cyclinder by taking "a" as the radius π(pie)a^2h

and I calculated the volume of the hemisphere (4/3πr^3)

and that was so far
 
Okay, using your formulas, we have the volume of a cylinder having radius $a$ as:

$$V_C=\pi a^2h$$

And the volume of a hemisphere of radius $a$ as:

$$V_H=\frac{2}{3}\pi a^3$$

Now, in order to find the volume of the given solid, we need to take the volume of the cylinder and remove (subtract) the volume of the hemisphere:

$$V_S=V_C-V_H$$

So, plug in for $V_C$ and $V_H$, then factor...what do you get?
 

Thread 'Area of Overlapping Squares'

Here is a little puzzle from the book 100 Geometric Games by Pierre Berloquin. The side of a small square is one meter long and the side of a larger square one and a half meters long. One vertex of the large square is at the center of the small square. The side of the large square cuts two sides of the small square into one- third parts and two-thirds parts. What is the area where the squares overlap?
View full post »

Similar threads

High School How to calculate a hollow cylinder's volume without the hollow center?
  • · Replies 7 ·
Replies
7
Views
2K
MHB Calculating Sand Volume for a Cylindrical Containment Vessel
  • · Replies 2 ·
Replies
2
Views
1K
Undergrad Volume of Solid of Revolution (About the line y = x)
  • · Replies 6 ·
Replies
6
Views
2K
MHB Find the volume of the hexagonal-shaped plastic box
  • · Replies 4 ·
Replies
4
Views
1K
MHB Calculate Volume & Surface Area of a Cylinder Without Lid
  • · Replies 4 ·
Replies
4
Views
2K
MHB Partial Volume of a Cylinder Calculation
  • · Replies 4 ·
Replies
4
Views
2K
MHB Volume of the solid obtained by rotating R around the line y=x
  • · Replies 2 ·
Replies
2
Views
2K
MHB Calculate volume of non parallel wedge
  • · Replies 1 ·
Replies
1
Views
2K
Volume of a cylinder and radius
  • · Replies 3 ·
Replies
3
Views
2K
MHB How to Maximize the Volume of a Cylinder with a Given Perimeter?
  • · Replies 3 ·
Replies
3
Views
4K