Answers

  1. Find the volume of the solid with circular base of diameter 10 cm and whose cross-sections perpendicular to a given diameter are equilateral triangles. [288.675]
  2. The base of a solid is the region bounded by the graph of and the x-axis. For this solid, each cross section perpendicular to the x-axis is a rectangle with height three times the base. What is the volume of this solid? [3.2]
  3. The base of a solid is the region in the first quadrant bounded by the x-axis, the y-axis, and the line , as shown in the figure. If cross sections of the solid perpendicular to the x-axis are semicircles, what is the volume of the solid? [C]
    A. 12.566 B. 14.661 C. 16.755
    D. 67.021 E. 134.041
  4. The region bounded by the graph of and the x-axis is the base of a solid. For this solid, each cross section perpendicular to the x-axis is an equilateral triangle. What is the volume of the solid? [D]
    A. 1.333 B. 1.067C. 0.577D. 0.462 E. 0.267
  5. The region in Quadrant I bounded by the graph of and is the base of a solid. Find the volume of this solid, if

(a)For this solid, each cross section perpendicular to the x-axis is an isosceles right triangle with one leg across the base of the solid. [0.016]

(b)For this solid, each cross section perpendicular to the x-axis is an isosceles right triangle with the hypotenuse across the base of the solid. [0.008]

  1. Let R be the region in Quadrant I bounded by the graph of , the y-axis, and the horizontal line .

(a)Find the area of R. [2.545]

(b)The region R is the base of a solid. For this solid, each cross section perpendicular to the y-axis is a square. Find the volume of this solid. [2.597]

  1. The base of a solid is the region in the first quadrant bounded by the y-axis, the graph of , the horizontal line , and the vertical line . For this solid, each cross section perpendicular to the x-axis is a square. What is the volume of the solid? [B]
    A. 2.561 B. 6.612 C. 8.046 D. 8.755 E. 20.773
  2. Let R be the region bounded by the graph of , the horizontal line , and the vertical line , as shown in the figure.

(a)Find the area of R. [3.310]

(b)The region R is the base of a solid. For this solid, each cross section perpendicular to the x-axis is a triangle with height equal to twice the length of the base. Find the volume of this solid. [4.722]

(c)Another solid whose base is also the region R. For this solid, each cross section perpendicular to the x-axis is a semicircle with diameter across the base. Find the volume of this solid. [1.854]

  1. Let R and S be the regions bounded by the graphs of and in Quadrant I.

(a)Find the total area of the regions bounded by f and g in Quadrant I, that is, . [1.077]

(b)Region R is the base of a solid. For this solid, each cross section perpendicular to the x-axis is an equilateral triangle. Find the volume of this solid. [0.165]

(c)Region S is the base of another solid. For this solid, each cross section perpendicular to the x-axis is a semicircle. Find the volume of this solid. [0.024]

  1. The region in Quadrant I bounded by the graphs of and is the base of a solid. For this solid, each cross section perpendicular to the y-axis is a rectangle with height four times the length of the width. Find the volume of this solid. [0.770]