Ask Question
25 September, 06:54

The base of S is the triangular region with vertices (0, 0), (1, 0), and (0, 1). Cross-sections perpendicular to the x-axis are squares. Find the volume V of this solid.

+2
Answers (1)
  1. 25 September, 10:11
    0
    the volume of the solid is V=1/6

    Step-by-step explanation:

    The solid S has a triangular cross section in the xy-plane with sides of length L=1. The boundaries are

    x=0

    y=0

    y = 1-x

    Since each cross section perpendicular to the x axis (parallel to the yz-plane) is a square then:

    z=x

    then the volume of the solid will be

    V = ∫dV=∫∫∫dxdydz ∫₀¹ (∫₀¹⁻ˣ dy) (∫₀ˣdz) dx = ∫₀¹ (1-x) * x dx = ∫₀¹ (x-x²) dx = [ (1/2) x² - (1/3) x³] |₀¹ = 1/2 - 1/3 = 1/6

    V=1/6
Know the Answer?
Not Sure About the Answer?
Find an answer to your question ✅ “The base of S is the triangular region with vertices (0, 0), (1, 0), and (0, 1). Cross-sections perpendicular to the x-axis are squares. ...” in 📘 Mathematics if you're in doubt about the correctness of the answers or there's no answer, then try to use the smart search and find answers to the similar questions.
Search for Other Answers