The radius of a sphere of lead (B = 4.2 × 10¹⁰ N/m²) is 1.000 m on the surface of the earth where the pressure is 1.01 × 10⁵ N/m². The sphere is taken by submarine to the deepest part of the ocean to a depth of 1.10 × 10⁴ m where it is exposed to a pressure is 1.25 × 10⁸ N/m². What is the volume of the sphere at the bottom of the ocean? A)4.176 m³ B)3.189 m³ C)2.251 m³ D)1.134 m³ E)0.988 m³

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Quizplus · Accepted Answer

The volume of a sphere is given by V = (4/3)πr^3. The radius of the sphere is given by r = 1.000 m. The pressure at the surface of the earth is given by P = 1.01 × 10^5 N/m^2. The pressure at the bottom of the ocean is given by P = 1.25 × 10^8 N/m^2. The bulk modulus of lead is given by B = 4.2 × 10^10 N/m^2. The change in volume of the sphere is given by ΔV = -BPΔr/r. The change in radius of the sphere is given by Δr = -BPΔV/r. The volume of the sphere at the bottom of the ocean is given by V = V0 + ΔV = (4/3)πr^3 - BPΔr/r = (4/3)πr^3 - BP(-BPΔV/r)/r = (4/3)πr^3 + B^2PΔV/r^3 = (4/3)π(1.000 m)^3 + (4.2 × 10^10 N/m^2)^2(1.25 × 10^8 N/m^2)(4.176 m^3)/(1.000 m)^3 = 4.176 m^3.

The Radius of a Sphere of Lead (B = 4