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After 4h: 2e6 - Appfinity Technologies

📅 March 1, 2026 👤 scraface

Mar 01, 2026

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📌 Question: A right circular cone has a base radius of $ 5x $ and a slant height of $ 13x $. What is the total surface area of the cone in terms of $ x $?

📌 Solution: The total surface area of a cone is the sum of the base area and the lateral surface area. The base area is:

📌 \pi (5x)^2 = 25\pi x^2.

📌 The lateral surface area is:

📌 \pi r \ell = \pi (5x)(13x) = 65\pi x^2.

📌 Total surface area:

📌 25\pi x^2 + 65\pi x^2 = 90\pi x^2.

📌 \boxed{90\pi x^2}

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The volume of a cube is $ V_{\text{cube}} = s^3 $. For the cube, $ s =...
V_{\text{cube}} = (6r)^3 = 216r^3
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\frac{V_{\text{cyl}}}{V_{\text{cube}}} = \frac{36\pi r^3}{216r^3} = \f...
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Question: A pharmacologist is modeling a spherical drug capsule of rad...
Solution: The volume of a hemisphere is $ V_{\text{hemisphere}} = \fra...
The volume of the cylinder is $ V_{\text{cyl}} = \pi r^2 h = \pi r^2 (...
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