A bowl is obtained by rotating the curve y = x^4 for -2 ≤ x ≤ 2 about the y-axis.
a) What is the volume of the bowl?
b) Suppose the bowl is filled with a liquid with mass 4/pi grams per cubic centimeter, and that x and y are given in centimeters. What is the total mass of the liquid in the bowl?
**please help will vote best answer thank you!!**
Copyright © 2024 1QUIZZ.COM - All rights reserved.
Answers & Comments
Verified answer
dV = pi x^2 dy
V = pi Int{y^(1/2)} dy
V = pi [2/3 y^(3/2)]. Between 0 and 2^4
V = pi 2/3 [(2^4)^(3/2) - 0]
V = pi 2/3 [64]
V =128 pi/3
Mass = V x 4/pi
M = 128 pi/3 x 4/pi
M = 512/3 grams
I can't see any errors but I expected more cancelling than happened there. Please check my working.