How Do You Compute the Volume of a Solid Bounded by Given Planes?

In summary, there are several online graphing utilities that can graph the solid bounded by the planes $x=7, z=y-2, z=-2y-2, z=0, \mbox{ and } z=2$.
  • #1
karush
Gold Member
MHB
3,269
5
Compute the volume of the solid bounded by the planes; $x=7, z=y-2, z=-2y-2, z=0, \mbox{ and } z=2$
Another source said the triple should be but Ii thought it should be $dx\,dy\,dz$
$$I = \displaystyle \int_0^7 \int_0^2 \int_{-\frac{z}{2} - 1}^{z+2} dy\,dz\,dx = 63$$
Hopefully this is the correct answer 😎

Is there an online graphing utility that would graph this?
 
Last edited by a moderator:
Physics news on Phys.org
  • #2

Yes, there are several online graphing utilities that can graph this solid for you. Some popular options include Desmos, GeoGebra, and WolframAlpha. Simply input the equations for each plane and adjust the viewing window to see the solid bounded by these planes.
 

FAQ: How Do You Compute the Volume of a Solid Bounded by Given Planes?

What is the definition of "Compute the Volume of the Solid"?

"Compute the Volume of the Solid" is a mathematical process used to determine the amount of space occupied by a three-dimensional object.

What are the steps involved in computing the volume of a solid?

The basic steps involved in computing the volume of a solid are:
1. Identify the shape of the solid, such as cube, cylinder, cone, etc.
2. Measure the dimensions of the solid, such as length, width, and height.
3. Use the appropriate formula for the given shape to calculate the volume.
4. Substitute the measured values into the formula and solve for the volume.
5. Round the answer to the appropriate number of significant figures.

What are some common formulas used to compute the volume of different solids?

Some common formulas used to compute the volume of different solids are:
1. Cube: Volume = (length)^3
2. Cylinder: Volume = π(radius)^2(height)
3. Sphere: Volume = (4/3)π(radius)^3
4. Cone: Volume = (1/3)π(radius)^2(height)
5. Pyramid: Volume = (1/3)(base area)(height)

What are some real-life applications of computing the volume of solids?

Some real-life applications of computing the volume of solids include:
1. Architecture: Architects use volume calculations to design and construct buildings and structures.
2. Manufacturing: Volume calculations are used in manufacturing to determine the amount of material needed to produce a certain number of products.
3. Packaging: Companies use volume calculations to determine the size and dimensions of packaging for products.
4. Agriculture: Farmers use volume calculations to determine the amount of soil and fertilizer needed for their crops.
5. Medicine: Doctors use volume calculations to determine the dosage of medication for patients based on their body weight.

What are some tips for accurately computing the volume of a solid?

To accurately compute the volume of a solid, consider the following tips:
1. Use the correct formula for the given shape.
2. Make sure to measure all dimensions accurately.
3. Use the appropriate units for measurement and ensure consistency throughout the calculation.
4. Double-check your calculations to avoid errors.
5. Round the final answer to the appropriate number of significant figures.
6. If the solid has irregular shapes, break it down into smaller, simpler shapes and add the volumes together.

Similar threads

MHB Triple Integrals: Finding Volume of Solid S Bounded by Planes
Replies
5
Views
2K
MHB *15.4.17 Volume between a cone and a sphere
Replies
2
Views
9K
MHB Finding Bounds for a Triple Integral: Solids Bounded by a Paraboloid and Plane
Replies
5
Views
2K
MHB What is the volume of the solid bounded by two paraboloids?
Replies
6
Views
2K
MHB Finding Bounds for a Triple Integral in the First Octant
Replies
10
Views
3K
MHB How to Set Up a Triple Integral for Volume Calculation?
Replies
8
Views
2K
MHB How to Set Up a Triple Integral for Volume in the First Octant?
Replies
5
Views
2K
MHB What are the y limits for finding the volume of a solid with given parameters?
Replies
5
Views
1K
I What if the Jacobian doesn't exist at finite points in domain of integral?
Replies
1
Views
1K
MHB M2215b.08 Find the volume of the solid (shell meithod)
Replies
8
Views
2K

Hot Threads

Recent Insights

Back
Top