AP Calculus AB Unit 8 Progress Check: MCQ Part B Flashcards | Knowt (2024)

The base of a solid is the region in the first quadrant bounded by the x- and y-axes and the graph of y=3−x/x+1. For the solid, each cross-section perpendicular to the x-axis is a rectangle whose height is twice its width in the xy-plane. What is the volume of the solid?

D. 7.819

The base of a solid is the region in the first quadrant bounded by the graph of y=cosx and the x- and y-axes for 0≤x≤π2. For the solid, each cross section perpendicular to the x-axis is an equilateral triangle. What is the volume of the solid?

A. 0.340

What is the volume of the solid generated when the region in the first quadrant bounded by the graph of y=√100−4x^2 and the x- and y-axes is revolved about the y-axis?

B. 523.599

Let R be the region in the first quadrant bounded by the graph of y=2tan(x/5), the line y=5−x, and the y-axis. What is the volume of the solid generated when RR is revolved about the line y=6?

D. 209.617

The base of a solid is the triangular region in the first quadrant bounded by the graph of y=4−2x and the x- and y-axes. For the solid, each cross section perpendicular to the x-axis is a square. What is the volume of the solid?

C. 32/3

Let R be the region in the first quadrant bounded by the graphs of y=x^2 and y=2x, as shown in the figure above. The region R is the base of a solid. For the solid, each cross section perpendicular to the x-axis is a square. What is the volume of the solid?

A. 16/15

Let R be the region in the first quadrant bounded by the graph of y=4e^x+2, the line x=1, and the x- and y-axes. R is the base of a solid whose cross sections perpendicular to the x-axis are semicircles. What is the volume of the solid?

A. π(e^2+2e−5/2)

Let R be the triangular region in the first quadrant, with vertices at points (0,0), (0,2), and (1,2). The region R is the base of a solid. For the solid, each cross section perpendicular to the y-axis is an isosceles right triangle with the right angle on the y-axis and one leg in the xy-plane. What is the volume of the solid?

A. 1/3

What is the volume of the solid generated when the region in the first quadrant bounded by the graph of y=x^3, the x-axis, and the vertical line x=2 is revolved about the x-axis?

D. 128π/7

What is the volume of the solid generated when the region in the first quadrant bounded by the graph of y=x^2, the y-axis, and the horizontal line y=1 is revolved about the y-axis?

C. π/2

Let R be the region bounded by the graph of y=lnx, the horizontal line y=1, and the vertical line x=1, as shown in the figure above. Which of the following gives the volume of the solid generated when the region R is revolved about the vertical line x=1?

C. π∫1-0 (e^y−1)^2ⅆy

Let R be the region enclosed by the graphs of y=5x−x^4 and the horizontal line y=3/2 The x-coordinates of the points of intersection of the graphs are x1 and x2, where x1<x2. Which of the following gives the volume of the solid generated when region R is revolved about the horizontal line y=3/2?

C. π∫x2-x1 (5x−x^4−3/2)^2dx

Let R be the region bounded by the graph of y=2x−2, the horizontal line y=2, and the vertical line x=1. Which of the following gives the volume of the solid generated when region R is revolved about the vertical line x=1?

B. π∫2-0 (y+2/2)−1)^2ⅆy

Let S be the region in the second quadrant bounded by the graphs of y=x^2ln(1−x^3) and y=−x, as shown in the figure above. The graphs intersect at x=A and x=0. Which of the following gives the volume of the solid generated when S is revolved about the line y=−1?

D. π∫0-A ((−x+1)^2−(x^2ln(1−x^3)+1)^2) dx

Let M be the region in the first quadrant bounded by the graph of y=3x+2, the graph of y=x+2, and the vertical line x=3. What is the volume of the solid generated when region M is revolved around the horizontal line y=1?

B. 90π

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