# What is Cross-sectional area: Definition and 23 Discussions

In geometry and science, a cross section is the non-empty intersection of a solid body in three-dimensional space with a plane, or the analog in higher-dimensional spaces. Cutting an object into slices creates many parallel cross-sections. The boundary of a cross-section in three-dimensional space that is parallel to two of the axes, that is, parallel to the plane determined by these axes, is sometimes referred to as a contour line; for example, if a plane cuts through mountains of a raised-relief map parallel to the ground, the result is a contour line in two-dimensional space showing points on the surface of the mountains of equal elevation.

In technical drawing a cross-section, being a projection of an object onto a plane that intersects it, is a common tool used to depict the internal arrangement of a 3-dimensional object in two dimensions. It is traditionally crosshatched with the style of crosshatching often indicating the types of materials being used.
With computed axial tomography, computers can construct cross-sections from x-ray data.

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1. ### I A smaller cross-sectional area increases the resistance of a conductor?

why smaller cross-sectional area increases the resistance of a conductor?
2. ### Buoyancy with the Cross-Sectional Area of a Rectangle

Hi all, My teacher assigned us a problem to do a few days ago and have attempted it many times, often leaving and coming back to see if I could figure it out. I imagine that you would take the cross-sectional area and multiply it by how far under the surface of the water the rectangular object...
3. ### Effective cross-sectional area

Hello sirs, How to calculate the cross-section area too toroid core? kindly explain this
4. ### I Differential cross-sectional area - Rutherford's experiment

I'm struggling to understand the importance of the differential cross-sectional area in Rutherford's scattering experiment, dσ/dθ. In one part of my course notes it is explained as 'the number of scatterings between θ and θ + dθ per unit flux, per unit range of angle'. However, dσ itself is...
5. ### Resistance, cross-sectional area of long coated wire

Homework Statement Homework Equations The Attempt at a Solution I attempted all of the parts: I think I did the right things for a-b-c-d, but I am pretty unsure about e & f. Can someone verify if my logic is right? Thanks.
6. ### Current through a conductor with varying cross-sectional area

Homework Statement Homework Equations I = nqVA J = E/ρ J = I/A The Attempt at a Solution The underlying assumption was that current was constant across all 3 bits of the conductor, and thus answer is b. The concept I can't grasp is this: Why is current constant? Shouldn't a smaller A mean...
7. ### Changing cross-sectional area effect on induced current

Recently I did an experiment where I dropped a magnet through a tube that was surrounded by a coil, and I hoped to investigate a factor that would affect the current induced (Faraday's law). I chose to study the effect that changing the cross-sectional area of the wire had on the induced...
8. ### Shell balances in cylindrical coordinates

Hello, PF! I have some doubts about setting up shell balances in a cylindrical geometry. Consider a fluid flowing down a vertical pipe. In order to perform the momentum balance, we take a cylindrical (annular) shell of length L and width Δr. The analysis of such system can be found in chapter 2...
9. ### Flux linkage in a wire coil

Flux linkage in a wire coil is given by BANcos(theta) with B being flux density, N being the number of turns in a coil and A being the cross sectional area of the coil and theta being the angle between the normal to the plane of the coil and the magnetic field. Is anybody able to explain why it...
10. ### Gibbs adsorption and cross-sectional area?

I am referring to the paper entitled "New Adsorption Model -Theory, Phenomena and New Concept - " which is published in J. Oleo Sci. (https://www.jstage.jst.go.jp/article/jos/64/1/64_ess14213/_article) I have question on your paper on paragraph 3 page 2 stating "The important finding is that...
11. ### Volume of Solid w/ 4x4 Square Base & Cross-Sections of Semicircles

Homework Statement Find the volume of the solid whose base is a 4 by 4 square. Cross sections perpendicular to one diagonal of the square base are semi-circles with diameter on the base. Homework Equations V=pi r^2 A=S^2 The Attempt at a Solution The cross sections are perpendicular to the x...
12. ### Finding cross-sectional area from terminal velocity.

Homework Statement The aerodynamic drag on an object moving through air is proportional to Av^2, where A=cross-section, and v=velocity. The terminal velocity of a person without a parachute falling through the air is about 56m/s. Estimate the area of the cross-section of a person seen from the...
13. ### Number of Wires & Cross-Sectional Area

Hi there, I'm a student in high school. I'm quite new to the forum. Please forgive my mistakes. Homework Statement My question is related to electricity, more specifically the factors affecting resistance in a wire. I know that resistance is inversely proportional to the cross-sectional...
14. ### Cross-sectional area for stress calculations

I am having a lot of difficulty calculating the cross-sectional areas necessary for normal/shear stress problems. If the cross-section is a square or circle, I'm fine, but when the problem makes a diagonal section through the object I get really confused on which angle/trig function to use to...
15. ### Is cross-sectional area of a coil related to it magnetic field strength

I have to desgin an experiment for physics and and my research question is going to be: How does the cross-sectional area of the solenoid’s coil affect the strength of its magnetic field? This is my hypothesis, my question is if you think the reasoning is valid. I believe I should find it is...
16. ### Volume computation (from cross-sectional area)

The base of each solid below is the region in the xy-plane bounded by the x-axis, the graph of $y=\sqrt{x}$ and the line x = 3. Find the volume of each solid. a) Each cross section is perpendicular to the y-axis is a square with one side in the xy-plane. b) Each cross section is...
17. ### Magnetic flux through the circular cross-sectional area of the solenoid

Homework Statement A solenoid 1.7 cm in diameter and 30 cm in length has 4000 turns and carries a current of 5 A. Calculate the magnetic flux(in Wb) through the circular cross-sectional area of the solenoid. Since this is a very long solenoid, you may use the simplified magnetic field formula...
18. ### Measuring cross-sectional area of a cable

How do we measure cross-sectional area of a cable (obviously circular)? For example, diameter of a cable as measured from vernier caliper was 19.5 mm. If we apply A = pi(3.14) r2, answer is 298.49 mm square but tag on said cable is showing Area = 10mm square? Please explain.
19. ### Oscillation of a Mass in Liquid (Densities and Cross-Sectional Area Known)

Homework Statement A body of uniform cross-sectional area A = 1 cm^2 and of mass density p = 0.8 g/cm^3 floats in a liquid of density p0 = 1 g/cm^3 and at equilibrium displaces a volume V = 0.8 cm^3. Show that the period of small oscillations about the equilibrium position is given by: T...
20. ### Find the cross-sectional area of a gutter

"A rain gutter is to be constructed from a metal sheet of width 30 cm by bending up one-third of the sheet on each side through an angle (theta) Show that the cross-sectional area of the gutter is modeled by the function A(theta)=100sin(theta)+100sin(theta)cos(theta)" My Question: what...
21. ### Smallest cross-sectional area of rod-end?

i was doing some reading on structural mechanics and i stumbled across this example: i don't really get the highlighted part. anyone care to explain? :)
22. ### Computing Volume from Cross-Sectional Area

Homework Statement A house attic has rectangular cross sections parallel to the ground and triangular cross sections perpendicular to the ground. The rectangle is 30 feet by 60 feet at the bottom of the attic and the triangles have base 30 feet and height 10 feet. Compute the volume of the...
23. ### Column cross-sectional area (cm2)

hello guys! i have a column with a shape of a cylinder. the radius is 2cm and the heigh is 5cm. i have to calculate the cross-sectional area of the column. i wonder what is the formula and how is the calculation? it has been a long time since i last had my math lectures, so i really hope for...