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Home » Derivative: \( f'(x) = 6x + 2 \) - DNSFLEX

Derivative: \( f'(x) = 6x + 2 \) - DNSFLEX

📅 March 11, 2026 👤 scraface

Mar 11, 2026

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For the original cone:
V_1 = \frac{1}{3} \pi (5)^2 (12) = \frac{1}{3} \pi \times 25 \times 12...
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...
The factor of increase is:
\frac{V_2}{V_1} = \frac{400\pi}{100\pi} = 4
Thus, the volume increases by a factor of:
\boxed{4}
Question:** A cylinder has a height equal to twice its radius. If the...
Let the original radius be \( r \), so the original height is \( h = 2...

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