(a) Use cylindrical coordinates to show that the volume of the solid bounded above by the sphere r 2 z 2 a 2 and below by the cone z r cot 0 (or 0 ), where 0 0 (b) Deduce that the volume of the spherical wedge given by (c) Use the Mean Value Theorem to show that the volume in part (b) can be written as

Question: (a) Use cylindrical coordinates to show that the volume of the solid bounded above by the sphere r 2 + z 2 = a 2

(a) Use cylindrical coordinates to show that the volume of the solid bounded above by the sphere r² + z² = a² and below by the cone z = r cot Φ₀ (or Φ = Φ₀), where 0 0

(b) Deduce that the volume of the spherical wedge given by

by the cone z = r cot Φ0 (or Φ = Φ0),

(c) Use the Mean Value Theorem to show that the volume in part (b) can be written as where 0 0 (b) Deduce that the volume of the spherical wedge

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