Chapter 5: Q19P (page 257)

In Problems 17 to 30, for the curve $y = \sqrt{x}$ , between $x = 0$ and $x = 2$ , find:
The volume of the solid generated when the area is revolved about the axis.

Short Answer

Expert verified

The volume of the solid is $2 π$ .

Step by step solution

Definition of the volume of solid

The space taken by a particular solid is measured by a special quantity known as the volume of the solid. The cubic units required to fill the space is the measure of the volume.

Representation of the area bounded by the curve

Draw the bounded region for the curve $y = \sqrt{x}$ , between $x = 0$ and $x = 2$ .

Determination of the volume of the solid generated when the area is revolved about the x -axis

Determine the value of elementary volume from the above figure.

$d V = π {(f (x))}^{2} = πx$

Determine the value of total volume.

$V = \int_{0}^{2} πxdx = \frac{π}{2} {[x^{2}]}_{0}^{2} = 2 π$

Thus, the volume of the solid is

2 π

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In Problems 17 to 30, for the curve $y = \sqrt{x}$ , between $x = 0$ and $x = 2$ , find:
The volume of the solid generated when the area is revolved about the axis.

Short Answer

Step by step solution

Definition of the volume of solid

Representation of the area bounded by the curve

Determination of the volume of the solid generated when the area is revolved about the x -axis

One App. One Place for Learning.

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In Problems 17 to 30, for the curve y=x, between x=0and x=2 , find:The volume of the solid generated when the area is revolved about the axis.

Short Answer

Step by step solution

Definition of the volume of solid

Representation of the area bounded by the curve

Determination of the volume of the solid generated when the area is revolved about the x -axis

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Physics Textbooks

Conservation of Energy and Momentum

Rotational Dynamics

Physical Quantities And Units

Electrostatics

Translational Dynamics

Wave Optics

Study anywhere. Anytime. Across all devices.

In Problems 17 to 30, for the curve $y = \sqrt{x}$ , between $x = 0$ and $x = 2$ , find:
The volume of the solid generated when the area is revolved about the axis.