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Home » Discover Every Secret Corner of Cape Cod with This Ultimate Map! - AMAZONAWS

Discover Every Secret Corner of Cape Cod with This Ultimate Map! - AMAZONAWS

Discover Every Secret Corner of Cape Cod with This Ultimate Map

📅 March 11, 2026 👤 scraface

Mar 11, 2026

Discover Every Secret Corner of Cape Cod with This Ultimate Map!

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📌 Question: An underwater archaeologist discovers a circular artifact partially submerged in water, forming a spherical cap with height $ h $ and base radius $ r $. If the full sphere from which the cap was formed has radius $ R $, what is the volume of the spherical cap in terms of $ h $, $ r $, and $ R $?

📌 Solution: The first 12 even numbers after 2020 are $2022, 2024, \ldots, 2044$. The sum of an arithmetic sequence is $S = rac{n}{2}(a_1 + a_n)$. Here, $n = 12$, $a_1 = 2022$, $a_n = 2044$. Thus, $S = rac{12}{2}(2022 + 2044) = 6 imes 4066 = 24396$. Dividing 24396 by 11: $11 imes 2216 = 24376$, so the remainder is $24396 - 24376 = 20$. However, $20 \mod 11 = 9$. Therefore, the remainder is $oxed{9}$.

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