# Centroid of solid enclosed by surface z= y^2 , plane x=0 ,

In summary, the conversation is about finding the centroid of a solid enclosed by a surface defined by z = y^2, with planes x = 0, x = 1, and z = 1. The density of the solid is 1. The person is attempting to use the equation Centroid = Mass of Inertia / Mass to solve the problem, but is unsure how to proceed with the given information.

## Homework Statement

Find the centroid of solid enclosed by surface z= y^2 , plane x=0 , x = 1 and z =1 . The density is 1

## The Attempt at a Solution

Here's my working .

Centoird = mass of inertia / mass
So , i find the mass first .

It's clear that the circle is on zx plane ... I am not sure whether to use z= rcos theta or z = rsin theta . Can you help ?

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## Homework Statement

Find the centroid of solid enclosed by surface z= y^2 , plane x=0 , x = 1 and z =1 . The density is 1

## The Attempt at a Solution

Here's my working .

Centoird = mass of inertia / mass
So , i find the mass first .

It's clear that the circle is on zx plane ... I am not sure whether to use z= rcos theta or z = rsin theta . Can you help ?
Almost everything you have here is wrong.
• Your drawing is way off. Take more time and get a more careful drawing the represents the solid described in your problem statement.
• "the circle is on zx plane" -- No, it's not a circle.
• You are apparently trying to use polar coordinates -- why?

## 1. What is the centroid of a solid enclosed by the surface z=y^2 and the plane x=0?

The centroid of a solid enclosed by the surface z=y^2 and the plane x=0 is the point at which the three coordinates of the solid intersect, dividing the solid into two equal parts. It is the center of mass of the solid and can be calculated by finding the average of the x, y, and z coordinates of all the points in the solid.

## 2. How is the centroid of a solid enclosed by the surface z=y^2 and the plane x=0 calculated?

The centroid of a solid enclosed by the surface z=y^2 and the plane x=0 is calculated by finding the average of the x, y, and z coordinates of all the points in the solid. This can be done by integrating the x, y, and z coordinates over the entire solid and dividing by the volume of the solid.

## 3. Is the centroid of a solid enclosed by the surface z=y^2 and the plane x=0 always located within the solid?

Yes, the centroid of a solid enclosed by the surface z=y^2 and the plane x=0 is always located within the solid. This is because the centroid is the average of all the points in the solid and therefore must be located within the solid itself.

## 4. How is the centroid of a solid enclosed by the surface z=y^2 and the plane x=0 used in engineering and physics?

The centroid of a solid enclosed by the surface z=y^2 and the plane x=0 is used in engineering and physics to calculate the center of mass of an object. This information is important for designing structures and predicting how they will behave under different conditions, such as when they are subjected to forces or movement.

## 5. Can the centroid of a solid enclosed by the surface z=y^2 and the plane x=0 be located outside of the solid?

No, the centroid of a solid enclosed by the surface z=y^2 and the plane x=0 will always be located within the solid. This is because the centroid is the average of all the points in the solid and therefore must be located within the solid itself.

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