Calculate the volume of the two sphere

  To calculate the volume of the larger sphere, we need to first determine the radius of both spheres using the formula for the surface area of a sphere: Surface Area of a Sphere = 4πr^2 Given that the surface areas of the two spheres are 36 cm^2 and 49 cm^2, we can set up the following equations: 1. For the smaller sphere: 36 = 4πr₁^2 r₁ = √(36 / 4π) ≈ √(9 / π) ≈ √(9 / 3.14) ≈ √2.87 ≈ 1.69 cm 2. For the larger sphere: 49 = 4πr₂^2 r₂ = √(49 / 4π) ≈ √(12.25 / π) ≈ √(12.25 / 3.14) ≈ √3.89 ≈ 1.97 cm Next, we can calculate the volume of the smaller sphere using the formula for the volume of a sphere: Volume of a Sphere = (4/3)πr^3 Given that the volume of the smaller sphere is 20.2 cm^3, we can set up the equation for the smaller sphere: 20.2 = (4/3)π(1.69)^3 20.2 = (4/3)π(4.77) 20.2 = 6.36π π ≈ 3.183 Now, we can calculate the volume of the larger sphere using the radius we found earlier: Volume of the larger sphere = (4/3)π(1.97)^3 Volume of the larger sphere ≈ (4/3) * 3.183 * 7.73 Volume of the larger sphere ≈ 10.64 * 7.73 Volume of the larger sphere ≈ 82.25 cm^3 Therefore, the volume of the larger sphere is approximately 82.25 cm^3.  

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