Calculus
7th Edition
ISBN: 9781524916817
Author: SMITH KARL J, STRAUSS MONTY J, TODA MAGDALENA DANIELE
Publisher: Kendall Hunt Publishing
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Chapter 12.7, Problem 54PS
To determine
To find: The volume of the solid
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4. (LO 7) A recangular box with a square base and an open top needs to have a volume
256
of 256 in?. The surface area of the box can be written as S(x) = 4x () + x², where
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the box? Include units.
2. Suppose you revolved the triangular region bound by the axes and
the line 4x + 3y
12 completely around the x-axis to sweep out
a solid of revolution. Describe the solid and then find its surface
area. Leave your answer exact.
5. The volume of the cube shown is x³ – 5x2 + 6x if one of
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Chapter 12 Solutions
Calculus
Ch. 12.1 - Prob. 1PSCh. 12.1 - Prob. 2PSCh. 12.1 - Prob. 3PSCh. 12.1 - Prob. 4PSCh. 12.1 - Prob. 5PSCh. 12.1 - Prob. 6PSCh. 12.1 - Prob. 7PSCh. 12.1 - Prob. 8PSCh. 12.1 - Prob. 9PSCh. 12.1 - Prob. 10PS
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- 2. Suppose that the triangle with vertices (-1,-1), (0, 1) and (1,–1) is revolved about the y – axis. Find the volume of the resulting solid.arrow_forward4. A solid has a circular base with equation x² + y² = 9. If every cross section perpendicular to the y-axis is an equilateral triangle, then its volume is (A) 36 (B) 12/3 (C) 18/3 (D) 24/3 (E) 36/3arrow_forward2. Find the volume of the largest rectangular box in the first octant with three faces in the coordinate planes and one vertex in the plane x+2y+z=2arrow_forward
- 12. A rectangular box with a square base and an open top must have a volume of 500 cm. The box should be constructed with a surface area as small as possible. Let I be the length, in cm, of the side-length of the base of the box. What should z be to minimize the surface area of the box? open top harrow_forward3. Determine the volume of the largest rectangular box in the first octant with three faces in the coordinate planes, one vertex at the origin, and its opposite vertex in the plane x+3y+6z = 36.arrow_forward3. Evaluate y³ +1 dydxarrow_forward
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