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Home » The side length of the square is \( \sqrt64 = 8 \) units. - AMAZONAWS

The side length of the square is \( \sqrt64 = 8 \) units. - AMAZONAWS

📅 March 5, 2026 👤 scraface

Mar 05, 2026

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📌 A conical vessel with a base radius of 3 cm and height of 9 cm is filled with water. What is the volume of water in cubic centimeters?

📌 Volume of a cone: \( V = \frac{1}{3} \pi r^2 h \).

📌 \( r = 3 \, \text{cm} \), \( h = 9 \, \text{cm} \).

📌 \( r^2 = 9 \), so \( V = \frac{1}{3} \pi \times 9 \times 9 = \frac{1}{3} \pi \times 81 = 27\pi \).

📌 Using \( \pi \approx 3.14159 \), \( V \approx 27 \times 3.14159 = 84.823 \).

📌 #### 84.82 cm³

📌 Solve for \( x \): \( 2^{x+1} = 16^{x-1} \).

📌 Express 16 as a power of 2: \( 16 = 2^4 \), so \( 16^{x-1} = (2^4)^{x-1} = 2^{4(x-1)} \).

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