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1/4 cup equals ounces - High Altitude Science

📅 March 10, 2026 👤 scraface

Mar 10, 2026

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📌 \( 120 = 3n(n+1) → n(n+1) = 40 → n ≈ 6.3 → n=6: 6×7=42>40, n=5:5×6=30<40 — no.

📌 n(n+1)=42 → n=6: 6×7=42 → then \( \frac{3×6×7}{2} = \frac{126}{2} = 63 \) — too big.

📌 Set Sₙ = 63, a=3, d=3

📌 \( 63 = \frac{n}{2}(6 + (n−1)3) = \frac{n}{2}(3n + 3) = \frac{3n(n+1)}{2} \)

📌 \( 126 = 3n(n+1) → n(n+1) = 42 → n=6:6×7=42 → yes!

📌 A cone has a base radius of 3 cm and a slant height of 5 cm. Using the formula \( V = \frac{1}{3}\pi r^2 h \), what is the volume in cubic centimeters when the height is calculated via Pythagoras?

📌 First, find height: \( h = \sqrt{l^2 - r^2} = \sqrt{25 - 9} = \sqrt{16} = 4 \

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