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📅 May 3, 2026 👤 scraface

May 03, 2026

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📌 A pyramid with a square base of side 6 cm and height 9 cm is filled with water. If this water is poured into a cone with a radius of 3 cm, what is the height of the water in the cone?

📌 Volume of pyramid = (1/3) × (6 cm)^2 × 9 cm = 108 cubic cm

📌 Volume of cone = (1/3)π × (3 cm)^2 × h = 3πh cubic cm

📌 Equating volumes: 108 = 3πh

📌 Solving for h: h = 108 / (3π) = 36 / π cm

📌 A rectangular prism has dimensions 8 cm by 6 cm by 4 cm. If a cylindrical hole with a radius of 1 cm is drilled through the center along the longest dimension, what is the remaining volume?

📌 Volume of prism = 8 cm × 6 cm × 4 cm = 192 cubic cm

📌 Volume of cylindrical hole = π × (1 cm)^2 × 8 cm = 8π cubic cm

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