Math 166 Exam 1-Review
Supplemental Instruction
Iowa State University
Leader:
Course:
Instructors:
Date:
Max and Jesse
Math 166
Dr. Lee and Dr. Martin
9/15/15
1) Find the volume of the solid obtained by rotating the region bounded between
y = 𝑥 2 and x = 𝑦 2 about the y-axis by using:
a. Shell Method
b. Washer Method
c. Rotate the same figure around the line x = -1. State the method that you
use.
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2) Find the Arc Length of the curve y = (3/4)x4/3 – (3/8)x2/3 +5, 1 ≤ x ≤ 8
3) Set up the integral you would use to find the surface area of the surface obtained
1
by rotating the curve 𝑦 = 𝑒 3𝑥 ( 0 ≤ 𝑥 ≤ 2 ) about the x-axis. Do not evaluate
the integral.
4) A spring that obeys Hooke’s Law (F = kx) has a natural length of 10 cm. If a 25 N
force is required to keep it stretched to a length of 20 cm, how much work is
required to stretch it from 10 cm to 15 cm?
5) Find the work done in pumping water to a height 5 ft. above the top of a conical
tank with a height of 20 ft. and a radius of 10 ft. (The cone is inverted, tank is full)
Use 𝛿 = 62.4.
6) Find the work done to pump water over the rim of a tank that is 40 feet long and
has semicircular ends of radius 8ft. The tank is half full of water. Use 𝛿 = 62.4.
7) Find the centroid of the region bounded by the curves:
𝑦 = 𝑥 2 𝑎𝑛𝑑 𝑦 = 𝑥 + 2