Flip a coin and toss a 1-6 number cube. Probability of: (heads and not a 3)
1 answer:
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Answer:
14π
Step-by-step 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
