The attachments are Calculus 2 quizzes they range from 15-10 questions the instructions are : Please extend sufficient space for solutions using the docx version, if you like to work on the quiz shee

MATH 141 Calculus II

Quiz 2

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Find the volume of the solid generated by revolving this region about the x-axis.

1. A base of a solid is the region bounded by , the x-axis, the y-axis, and the line Each cross-section perpendicular to the x-axis is a square. Find the volume of the solid.

1. The base of a solid is the disk bounded by the circle . Find the volume of the solid given that the cross-sections perpendicular to the x-axis are squares.

For problems 5 and 6, find the volume of the solid generated by revolving this region about the y-axis.

(Hint: draw a picture.)

1. The force of gravity exerted by the Earth on a mass m at a distance r from the center of the Earth is given by Newton’s formula,

,

where M is the mass of the Earth and G is the universal gravitational constant. Find the work done by gravity in pulling a mass m from to .

1. Find the work done by a force F, in pounds, that moves a particle along the x-axis from feet to feet, if .

1. A cylindrical reservoir of diameter 4 feet and height 6 feet is half-full of water weighing w pounds per cubic feet. Find the work done in emptying the water over the top.

1. Find the area of the surface generated by revolving the curve about the x-axis.

1. Calculate the length of the arc .

1. Find the centroid of the region bounded between the graph , x-axis, and the vertical line .