Calculus
6th Edition
ISBN: 9781465208880
Author: SMITH KARL J, STRAUSS MONTY J, TODA MAGDALENA DANIELE
Publisher: Kendall Hunt Publishing
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Chapter 12.5, Problem 27PS
To determine
To find:the volume of the solid bounded by the graphs of given equations.
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5. Find the exact value (no decimals) of the volume of the solid whose base is the triangle with vertices
(0, 0), (0, 10), and (5, 0) and whose cross sections taken perpendicular to the x-axis are squares.
page 5
1) Find the AREA
and VOLUME (Identify what type of volume)
bounded by the equations; y = 4x – x² and x+ y = 4 rotated at
x-axis.
jand y-axis
No Graph, No Strip or Incomplete graph. and No solution means wrong answer!
2.
A manufacturer needs to make a cylindrical can that uses 100 square centimeters of material. Determine the
radius of the can that will maximize the volume of the can.
For a cylinder, V
πr?h and Α= 2πrh+ 2πr?
= T
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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- 3. Find the volumes of the solids generated by revolving the regions bounded by the graphs of the equations about the given lines. y = 5x2 y = 0 x = 3 (a) the y-axis (b) the x-axis (c) the line y = 45 (d) the line x = 3arrow_forward(b) insects per cubic foot. Describe the set of all points at which the insect density is 20 (c) shape of the level surfaces? Describe the level surfaces of the function p. Identify the generalarrow_forward14. A calculator may be used to solve this problem. Round to three decimal places. Find the volume of the solid that results when the region enclosed by the curves y= -x²+6, y=2, and x-0 is revolved around the axis x=-3. *arrow_forward
- 4. 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_forwardAnswer B b. how do the dimensions of the least expensive can change if the bottom material cost more tha 5 cent per square inch? 7. (a) Determine the dimensions of the least expesive cylindrical can the will hold 100 cubic inches if the materials cost 2 cent , 5 cent and 3 cent, respectively, for the top, bottom ad sides. b. how do the dimensions of the least expensive can change if the bottom material cost more tha 5 cent per square inch?arrow_forwardProblem. 22: Use a double integral to find the volume of the solid shown in the figure. 2=6-Y 4. ? cubic units 3.arrow_forward
- 5. Find the volume of the solid generated by revolving about the x-axis the smaller area bounded by the equation x2+y²=2 and the semi-cubical parabola y3=x2. 6. Show that when a hole of radius a is bored through the center of the sphere of radius b, the volume of the sphere that is left is V= (4T/3)(b² - a²)(3/2)arrow_forward2. The figure shows the curves of the equations: y = 2x², y = 4x - 2, and y = 8. Find the volume of the solid obtained by rotating the region bounded by the three curves about the y-axis. (Just express it as an integral formula, and its value does not to be calculated.) (a) Use the method of washers (b) Use the method of cylindrical shells (Hint: You need divide the region into two parts first.)arrow_forward4. A restaurant is being built on the side of a mountain, the plans are shown below. (a) The vertical curved wall of the restaurant is to be built of glass. What will be the surface area of this wall? (b) To be large enough to be profitable, the consulting engineer informs the developer that the volume of the interior must exceed TR¹/2. For what R does the proposed structure satisfy this requirement? (c) During a typical summer day, the environs of the restaurant are subject to a tempertaure field given by T(x, y, z) = 3x² + (y− R)² + 16z². A heat flux density V = -kVT (k is a constant depending on the grade of the insulation to be used) through all sides of the restaurant (including the top and the contact with the hill) produces a heat flux. What is the total heat flux? (Your answer will depend on R and k.) x² + y² +z =4R² 2R side view R restaurant y x² + y²-4R² 2R top view x² + (y-R)² = R² R yarrow_forward
- 2. Ahmed and Rami are finding the surface area of a cylinder with a height of 7 cm and a radius of 10 cm. Is either of them, correct? Explain your answer Ahmed Rami S = π(10)²+ π(10)(7) S = 2π(7)² + 2π(10)(7) S = 10 + 70π S = 98T + 140m S = 80 cm² S = 238 π cm² TTarrow_forwardCalculate the area of the smaller region (to the left of the parabola) bounded by (x + 5)² = 2y, the x-axis, and the line tangent to the circle x² + y²=25 at (3,4). O 15.21 square units 33.43 square units O 43.23 square units 22.89 square unitsarrow_forwardCalculate the area of the smaller region (to the left of the parabola) bounded by (x+5)2=2y, the x-axis, and the line tangent to the circle x2 + y2=25 at (3,4). O 22.89 square units 43.23 square units 33.43 square units O 15.21 square unitsarrow_forward
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