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Home » "What is a Neck Hump? The Shocking Truth Behind This Silent Discomfort! - Upplift

"What is a Neck Hump? The Shocking Truth Behind This Silent Discomfort! - Upplift

📅 February 28, 2026 👤 scraface

Feb 28, 2026

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📌 A glaciologist is modeling a glacier as a truncated cone with a top radius of $3r$ and a bottom radius of $r$, with a height of $h$. If the volume of the glacier is $V$, express $V$ in terms of $r$ and $h$ and find the volume when $r = 2$ and $h = 5$.

📌 The volume \( V \) of a truncated cone is given by the formula:

📌 \[ V = \frac{1}{3} \pi h (R_1^2 + R_1 R_2 + R_2^2) \]

📌 where \( R_1 \) is the top radius and \( R_2 \) is the bottom radius. Here, \( R_1 = 3r \) and \( R_2 = r \). Substituting these into the formula, we get:

📌 \[ V = \frac{1}{3} \pi h ((3r)^2 + (3r)(r) + r^2) \]

📌 \[ V = \frac{1}{3} \pi h (9r^2 + 3r^2 + r^2) \]

📌 \[ V = \frac{1}{3} \pi h (13r^2) \]

📌 \[ V = \frac{13}{3} \pi hr^2 \]

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