A solid has a base in the form of an ellipse with major axis 10 and minor axis 8. Find its volume if every section perpendicular to the major axis is an isosceles right triangle with one leg in the plane of the base. Ans. 640/3 cubic units
A solid has a base in the form of an ellipse with major axis 10 and minor axis 8. Find its volume if every section perpendicular to the major axis is an isosceles right triangle with one leg in the plane of the base. Ans. 640/3 cubic units
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:A solid has a base in the form of an ellipse with major axis 10 and minor axis 8. Find its volume if every
section perpendicular to the major axis is an isosceles right triangle with one leg in the plane of the
base.
Ans. 640/3 cubic units
The base of a solid is the segment of the parabola y 12x cut off by the latus rectum. A section of the
solid perpendicular to the axis of the parabola is a square. Find its volume.
%3D
Ans. 216 cubic units
The base of a solid is the first-quadrant area bounded by the line 4x + 5y = 20 and the coordinate axes.
Find its volume if every plane section perpendicular to the x axis is a semicircle.
Ans.
107/3 cubic units
The base of a solid is the circle x+ y 16x, and every plane section perpendicular to the x axis is a
rectangle whose height is twice the distance of the plane of the section from the origin. Find its
volume.
%3D
Ans. 1024 T cubic units
A horn-shaped solid is generated by moving a circle, having the ends of a diameter on the first-quadrant
arcs of the parabolas y+ 8x = 64 and y + 16x = 64, parallel to the xz plane. Find the volume
generated.
Ans. 256 7/15 cubic units
The vertex of a cone is at (a, 0,0), and its base is the circle y+ z- 2by 0, x = 0. Find its
volume.
Ans. rab? cubic units
Find the volume of the solid bounded by the paraboloid y + 4z x and the plane x = 4.
Ans.
47 cubic units
A barrel has the shape of an ellipsoid of revolution with equal pieces cut from the ends. Find its volume
if its height is 6 ft, its midsection has radius 3 ft, and its ends have radius 2 ft.
Ans. 44 7 ft
The section of a certain solid cut by any plane perpendicular to the x axis is a circle with the ends of a
= 9x and x = 9y. Find its volume.
diameter lying on the parabolas y
Ans. 6561 7 /280 cubic units
The section of a certain solid cut by any plane perpendicular to the x axis is a square with the ends of a
diagonal lying on the parabolas y = 4x and x = 4y. Find its volume.
Ans. 144/35 cubic units
A hole of radius 1 inch is bored through a sphere of radius 3 inches, the axis of the hole being a diameter
of the sphere. Find the volume of the sphere which remains.
Ans. 64 V2/3 in'
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