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Home » Sum of roots is \( 3 + 5 = 8 \), so \( -\fracba = 8 \). - Crosslake

Sum of roots is \( 3 + 5 = 8 \), so \( -\fracba = 8 \). - Crosslake

📅 March 1, 2026 👤 scraface

Mar 01, 2026

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📌 For the hemisphere with radius \(6\) units:

📌 V_{\text{hemisphere}} = \frac{2}{3} \pi (6)^3 = \frac{2}{3} \pi \times 216 = 144\pi

📌 The ratio of the volume of the sphere to the volume of the hemisphere is:

📌 \text{Ratio} = \frac{V_{\text{sphere}}}{V_{\text{hemisphere}}} = \frac{36\pi}{144\pi} = \frac{1}{4}

📌 Thus, the ratio of the volume of the sphere to the volume of the hemisphere is \(\boxed{\frac{1}{4}}\).

📌 A high school student is designing a garden with a circular pond and a semicircular walkway around it. If the radius of the pond is \(r\) units and the radius of the walkway is \(5r\) units, what is the ratio of the area of the pond to the area of the walkway?

📌 To find the ratio of the areas, we calculate the area of each shape.

📌 The area \(A\) of a circle with radius \(r\) is given by:

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