Looking for trustworthy answers? Westonci.ca is the ultimate Q&A platform where experts share their knowledge on various topics. Connect with a community of professionals ready to help you find accurate solutions to your questions quickly and efficiently. Discover detailed answers to your questions from a wide network of experts on our comprehensive Q&A platform.
Sagot :
The volume of the described solid is V = 16r³/3
Given,
A solid line S should be drawn between z=a and z=b. If S has a cross-sectional area of Px through x and is perpendicular to the x-axis, then A (x)
Volume of S = limₙ→∝ ∑i=₁ⁿ A(xi) Δx = [tex]\int\limits^b_a {A(x)} \, dx[/tex]
The equation of circle x² + y² = r² where r is the radius of the circle.
Equation of upper semicircle yu= √(r²-x²) and
Equation of lower semicircle yl = -√(r²-x²)
Area of cross-section A(x) = (yu² - yl²)
Substitute yu and yl values
A(x) = [√(r²-x²) - (-√(r²-x²) )]² = 4(r² -x²) (1)
The limit for volume v varies from -r to r
Thus Volume v = ₋[tex]\int\limits^r_r {A(x)} \, dx[/tex]
Substitute A(x) from (1)
V = ₋[tex]\int\limits^r_r {4(r^{2}-x^{2} ) } \, dx[/tex]
⇒V = 4[r²x - x³/3 ]
⇒V = 4(r³ - r³/3) - 4(-r³ + r³/3) = 4[2 (r³ - r³/3)] = 16r³/3
The volume of the described solid S where the base is a circular disk or radius r and parallel cross sections perpendicular to the base are squares is V = 16r³/3
Learn more about volume of solid here;
https://brainly.com/question/29061740
#SPJ4
Thank you for your visit. We're committed to providing you with the best information available. Return anytime for more. We appreciate your time. Please come back anytime for the latest information and answers to your questions. Your questions are important to us at Westonci.ca. Visit again for expert answers and reliable information.
