Answer:
14π
Explanation:
Graph the region. Rotated about the y-axis, the volume is a round, spherical shape.
Slice the volume into a vertical stack of discs. The radius of each disc is x, the thickness of each disc is dy. The volume of each disc is:
dV = π x² dy
dV = π (7 sin y) dy
dV = 7π sin y dy
The total volume is the sum of all the discs from y=0 to y=π.
V = ∫ dV
V = ∫₀ᵖⁱ 7π sin y dy
V = -7π cos y |₀ᵖⁱ
V = -7π (cos π − cos 0)
V = -7π (-1 − 1)
V = 14π