# Compute the volume of another solide

• number0
In summary, the volume of a solid is calculated by multiplying the area of its base by its height, using the formula V = Bh. The unit of measurement for volume depends on the unit of measurement used for the dimensions of the solid. The volume of a solid cannot be negative, as it is a measure of the amount of space occupied by the solid. Some common shapes used to represent solids include cubes, cylinders, spheres, cones, and pyramids. The density of a solid does not affect its volume, as volume is a measure of space while density is a measure of mass.
number0

## Homework Statement

Compute the volume of the solid bounded by the surface z = sin(y), the planes x = 1, x = 0, y = 0, and y = pi/2, and the xy plane.

None.

## The Attempt at a Solution

Double Integral sin(y) dA

where the limits of integration is:

0 </ x </ 1

0 </ y </ pi/2

After calculating the double integral, I got 1. Can anyone verify my work?

number0 said:
After calculating the double integral, I got 1. Can anyone verify my work?

I get V = 1 as well.

## 1. How is the volume of a solid calculated?

The volume of a solid is calculated by multiplying the area of its base by its height. This method is also known as the formula V = Bh, where B represents the base and h represents the height.

## 2. What is the unit of measurement for volume?

The unit of measurement for volume depends on the unit of measurement used for the dimensions of the solid. For example, if the dimensions are in meters, then the volume will be in cubic meters (m3). If the dimensions are in inches, then the volume will be in cubic inches (in3).

## 3. Can the volume of a solid be negative?

No, the volume of a solid cannot be negative. Volume is a measure of the amount of space occupied by a solid, and it cannot have a negative value.

## 4. What are some common shapes used to represent solids?

Some common shapes used to represent solids include cubes, cylinders, spheres, cones, and pyramids. These shapes have known formulas for calculating their volume.

## 5. How does the density of a solid affect its volume?

The density of a solid does not affect its volume. Volume is a measure of the amount of space occupied by a solid, while density is a measure of how much mass is contained in a certain volume. Therefore, the volume of a solid remains the same regardless of its density.

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