2. A rectangular metal box of dimensions 4, 8 and 12 units was heated and its dimensions were changed to 4.01, 8.02 and 12.03 respectively. Use the total differential to find the approximate change in the volume of the box. [The volume of a rectangular box is V =lw h].
2. A rectangular metal box of dimensions 4, 8 and 12 units was heated and its dimensions were changed to 4.01, 8.02 and 12.03 respectively. Use the total differential to find the approximate change in the volume of the box. [The volume of a rectangular box is V =lw h].
Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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Transcribed Image Text:2. A rectangular metal box of dimensions 4, 8 and 12 units was heated and its dimensions were changed
to 4.01, 8.02 and 12.03 respectively. Use the total differential to find the approximate change in the
volume of the box. [The volume of a rectangular box is V =lwh.
3. Find the dimensions of the rectangular box of maximum volume that has three sides in the coordinate
planes, one vertex at the origin, and one vertex in the first octant on the plane 6x + 3y + 2z = 18. (9
4. Let S be the solid bounded below by the ry-plane, above by the plane r+y + z = 2, and laterally
by the cylinder y = x.
(a) Sketch the solid.
(b) Find the volume of the solid.
5. Let S be the solid bounded below by the ry-plane, above by the half-cone z =
2+ y?, and
laterally by the cylinder (r 1)2 +y² = 1.
(a) Sketch the solid.
(b) Find the volume of the solid.
6. Let S be the solid lying outside the cone z = r² + y² (the portion containing the ry-plane), outside
the cylinder r? +y? = 1, and inside the sphere r² + y² + z? = 4.
(a) Sketch the solid.
(b) Use spherical coordinates to find the volume of the solid.
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