Homework SourseThe base of a solid is bounded by yX2 and y1 Find the volume
The base of a solid is bounded by y=X^2 and y=1.
Find the volume of the solid formed if cross sections are square perpendicular to the y-axis
Find the volume of the solid formed if cross sections are square perpendicular to the y-axis
Solution
y = x^2 and line y = 1 intersect x² = 1 x = ±1 Use disk method, where each cross-section perpendicular to axis y=1 has radius r = 1 - x² V = p ??1¹ r² dy V = p ??1¹ (1 - x²)² dy V = p ??1¹ (1 - 2x² + x4) dy V = p (y - 2x³/3 + x5/5) |?1¹ V = p ((1 - 2/3 + 1/5) - (-1 + 2/3 - 1/5)) V = p ((8/15) - (-8/15)) V = 16p/15
