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Home » So, revise: The cost function is \( C(x) = 5000 - 500apps

So, revise: The cost function is \( C(x) = 5000 - 500apps

📅 March 13, 2026 👤 scraface

Mar 13, 2026

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📌 Question:** A right circular cone has a height of 12 cm and a base radius of 5 cm. If the radius is doubled while the height remains the same, by what factor does the volume increase?

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

📌 V = \frac{1}{3} \pi r^2 h

📌 For the original cone:

📌 V_1 = \frac{1}{3} \pi (5)^2 (12) = \frac{1}{3} \pi \times 25 \times 12 = 100\pi \text{ cm}^3

📌 When the radius is doubled to 10 cm, the new volume \( V_2 \) is:

📌 V_2 = \frac{1}{3} \pi (10)^2 (12) = \frac{1}{3} \pi \times 100 \times 12 = 400\pi \text{ cm}^3

📌 The factor of increase is:

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