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📅 May 2, 2026 👤 scraface

May 02, 2026

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📌 A rectangular garden measures 15 meters by 10 meters. If a path 1 meter wide is built inside along the perimeter, what is the area of the remaining garden space?

📌 The dimensions of the path-reduced garden are reduced by 2 meters in each dimension (1 meter on each side), resulting in dimensions of 13 meters by 8 meters. The area of the remaining garden is 13 * 8 = 104 square meters.

📌 A cylindrical tank with a radius of 3 meters and a height of 5 meters is filled with water. If a solid sphere with a radius of 2 meters is submerged in the tank, by how many cubic meters does the water level rise?

📌 The volume of the sphere is calculated using the formula \( \frac{4}{3} \pi r^3 \). For a radius of 2 meters, the sphere's volume is \( \frac{4}{3} \pi (2)^3 = \frac{32}{3} \pi \) cubic meters. This volume matches the rise in water level in the tank.

📌 #### \(\frac{32}{3} \pi\)

📌 A company sells two products: A and B. Product A costs $50, and 40% of sales are Product A. Product B costs $70. If total revenue from 100 units sold is $6,500, how many units of Product B were sold?

📌 Let \( x \) be the number of Product B units sold. Then, \( 100 - x \) units are Product A. Revenue equation: \( 50(100 - x) + 70x = 6500 \). Solving: \( 5000 - 50x + 70x = 6500 \) simplifies to \( 20x = 1500 \), so \( x = 75 \).

📌 A bank account earns 5% annual interest, compounded annually. If $2,000 is deposited, how much will the account hold after 3 years?

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