Subjects geometry

Sandbox Sand 841B2D

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1. **State the problem:** We need to find the volume of sand required to fill a square sandbox with inside dimensions 6 ft by 6 ft and wall height 9 inches, but the sand height is 1 inch less than the wall height. 2. **Convert all measurements to consistent units:** - Wall height = 9 inches - Sand height = 9 inches - 1 inch = 8 inches - Convert inches to feet: 1 foot = 12 inches - Sand height in feet = $\frac{8}{12} = \frac{2}{3}$ feet 3. **Calculate the volume of sand:** - Volume $V = \text{length} \times \text{width} \times \text{height}$ - $V = 6 \times 6 \times \frac{2}{3} = 36 \times \frac{2}{3} = 24$ cubic feet 4. **Calculate the cost of sand before tax:** - Cost per cubic foot = 11.50 - Total cost before tax = $24 \times 11.50 = 276$ 5. **Calculate total tax:** - GST = 5% = 0.05 - PST = 7% = 0.07 - Total tax rate = 0.05 + 0.07 = 0.12 6. **Calculate total cost after tax:** - Total cost after tax = $276 \times (1 + 0.12) = 276 \times 1.12 = 309.12$ **Final answers:** - Volume of sand required = 24 cubic feet - Price of sand after taxes = 309.12