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Home » \[ h(t) = h_0 - rt^2. \] - 500apps

\[ h(t) = h_0 - rt^2. \] - 500apps

📅 March 14, 2026 👤 scraface

Mar 14, 2026

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📌 \sin 180^\circ - \sin 45^\circ = 0 - \frac{\sqrt{2}}{2} = -\frac{\sqrt{2}}{2}

📌 The simplified expression is:

📌 Question:** The radius of a sphere is \(2x\) units and the radius of a hemisphere is \(3x\) units. What is the ratio of the volume of the hemisphere to the volume of the sphere?

📌 The volume \(V_{\text{sphere}}\) of a sphere with radius \(r\) is:

📌 V_{\text{sphere}} = \frac{4}{3}\pi r^3

📌 For the sphere with radius \(2x\):

📌 V_1 = \frac{4}{3}\pi (2x)^3 = \frac{4}{3}\pi (8x^3) = \frac{32}{3}\pi x^3

📌 The volume \(V_{\text{hemisphere}}\) of a hemisphere with radius \(r\) is half the volume of a full sphere:

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