Find the volume of a described solid

  • Thread starter Thread starter Physicsisfun2005
  • Start date Start date
  • Tags Tags
    Solid Volume
AI Thread Summary
The discussion focuses on calculating the volume of a solid with a base defined by the equation x^2+y^2=9, where the cross sections are isosceles right triangles. The user presents their volume calculation as π∫(4.5 - 0.5x^2) dx from -3 to 3, arriving at a volume of 18π. Other participants confirm the user's approach and calculations, suggesting that graphing the region and cross sections can help verify the results. They recommend double-checking the integration for accuracy. Overall, the consensus is that the user's method and final answer appear correct.
Physicsisfun2005
Messages
70
Reaction score
0
I don't have the answers in the back of my book and I really want to know if i did this correctly since its graded. the Problem is: Let the region bounded by x^2+y^2=9 be the base of a solid. Find the Volume if cross sections taken perpendicular to the base are isosceles right triangles.
i know a triangle is .5bh and the base of it will be \sqrt{9-x^2} so for volume the final answer is \pi\int 4.5-.5x^2 dx with the limits from -3 to 3 and i get 18\pi for volume.....is this right?
 
Last edited:
Physics news on Phys.org


Your calculation looks correct to me! To double check, you can graph the region and the cross sections to make sure they match up with your calculations. Also, it never hurts to double check your integration and make sure you didn't make any mistakes. But overall, it looks like you have the right approach and answer. Great job!
 
Thread 'Variable mass system : water sprayed into a moving container'

Thread 'Variable mass system : water sprayed into a moving container'

Starting with the mass considerations #m(t)# is mass of water #M_{c}# mass of container and #M(t)# mass of total system $$M(t) = M_{C} + m(t)$$ $$\Rightarrow \frac{dM(t)}{dt} = \frac{dm(t)}{dt}$$ $$P_i = Mv + u \, dm$$ $$P_f = (M + dm)(v + dv)$$ $$\Delta P = M \, dv + (v - u) \, dm$$ $$F = \frac{dP}{dt} = M \frac{dv}{dt} + (v - u) \frac{dm}{dt}$$ $$F = u \frac{dm}{dt} = \rho A u^2$$ from conservation of momentum , the cannon recoils with the same force which it applies. $$\quad \frac{dm}{dt}...
View full post »

Similar threads

Ice Core Density Problem (Inspired by NEEM)
Replies
6
Views
513
Find Isobaric Expansion & Pressure-Volume Coefficient for Solid
Replies
4
Views
1K
Finding the center of mass of a solid hemisphere
Replies
19
Views
3K
Calculating the Solid Angle of a Nebula from Earth
Replies
5
Views
2K
How Does the Equation of State for a Solid Change with Temperature and Pressure?
Replies
5
Views
3K
Depth of a basketball floating on water
Replies
9
Views
879
Will the displacement of a solid ball affect the water level?
Replies
7
Views
2K
Probability of finding a pion in a small volume of pionic hydrogen
Replies
6
Views
2K
Calculating the volume of the solid in this graph
Replies
4
Views
1K
Solid angle in an optics problem (artificial irradiance of the Earth)
Replies
15
Views
2K

Hot Threads

Recent Insights

Back
Top