# Volumes

## Calculus 2 / Bc ### 250 Practice Problems

03:30 Essential Calculus Early Transcendentals

Find the volume of the described solid $S .$
The base of $S$ is the same base as in Exercise $42,$ but cross-sections perpendicular to the $x$ -axis are isosceles triangles
with height equal to the base.

APPLICATIONS OF INTEGRATION
Volumes 02:26 Essential Calculus Early Transcendentals

Find the volume of the described solid $S .$
The base of $S$ is the same base as in Exercise 40 , but cross-sections perpendicular to the $x$ -axis are squares.

APPLICATIONS OF INTEGRATION
Volumes 06:01 Essential Calculus Early Transcendentals

Each integral represents the volume of a solid. Describe the solid.
$$\text { (a) }\pi \int_{0}^{\pi / 2} \cos ^{2} x d x \quad \text { (b) } \pi \int_{0}^{1}\left(y^{4}-y^{8}\right) d y$$

APPLICATIONS OF INTEGRATION
Volumes 01:19 Essential Calculus Early Transcendentals

Find the volume of the described solid $S .$
A pyramid with height $h$ and rectangular base with dimensions $b$ and 2$b$

APPLICATIONS OF INTEGRATION
Volumes 01:00 Essential Calculus Early Transcendentals

Find the volume of the described solid $S .$
A right circular cone with height $h$ and base radius $r$

APPLICATIONS OF INTEGRATION
Volumes 05:23 Essential Calculus Early Transcendentals

Set up an integral for the volume of the solid obtained by rotating the region bounded by the given curves about the specified line. Then use your calculator to evaluate the integral correct to five decimal places.
$$y=x^{2}, x^{2}+y^{2}=1, y \geqslant 0$$
(a) About the $x$ -axis (b) About the $y$ -axis

APPLICATIONS OF INTEGRATION
Volumes 02:58 Essential Calculus Early Transcendentals

A CAT scan produces equally spaced cross-sectional views
of a human organ that provide information about the organ
otherwise obtained only by surgery. Suppose that a CAT
scan of a human liver shows cross-scctions spaced 1.5 $\mathrm{cm}$
apart. The liver is 15 $\mathrm{cm}$ long and the cross-sectional areas,
in square centimeters, are $0,18,58,79,94,106,117,128,$
$63,39,$ and $0 .$ Use the Midpoint Rulc to estimate the volume of the liver.

APPLICATIONS OF INTEGRATION
Volumes 03:51 Essential Calculus Early Transcendentals

The region enclosed by the given curves is rotated about the specified line. Find the volume of the resulting solid.
$$y=x^{3}, y=\sqrt{x} ; \quad \text { about } y=1$$

APPLICATIONS OF INTEGRATION
Volumes 04:03 Essential Calculus Early Transcendentals

The region enclosed by the given curves is rotated about the specified line. Find the volume of the resulting solid.
$$y=x^{3}, y=\sqrt{x} ; \quad \text { about } x=1$$

APPLICATIONS OF INTEGRATION
Volumes 02:54 Essential Calculus Early Transcendentals

The region enclosed by the given curves is rotated about the specified line. Find the volume of the resulting solid.
$$x=y^{2}, x=1 ; \quad \text { about } x=1$$

APPLICATIONS OF INTEGRATION
Volumes 04:10 Essential Calculus Early Transcendentals

The region enclosed by the given curves is rotated about the specified line. Find the volume of the resulting solid.
$$x-y=1, y=x^{2}-4 x+3 ; \quad \text { about } y=3$$

APPLICATIONS OF INTEGRATION
Volumes 03:10 Essential Calculus Early Transcendentals

The region enclosed by the given curves is rotated about the specified line. Find the volume of the resulting solid.
$$x=2 y-y^{2}, x=0 ; \quad \text { about the } y-axis$$

APPLICATIONS OF INTEGRATION
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