Andrea is making a sandbox for her children. She has made a wooden frame for her backyard that is 11 feet long, 8 feet wide, and 2 feet deep. She can purchase sand for the sandbox for $30 per cubic meter. How much will it cost Andrea to purchase sand? (Hint: 1 foot = 0.3048 meters.)(Round your answer to the nearest dollar.)
Question
Andrea is making a sandbox for her children. She has made a wooden frame for her backyard that is 11 feet long, 8 feet wide, and 2 feet deep. She can purchase sand for the sandbox for $30 per cubic meter. How much will it cost Andrea to purchase sand? (Hint: 1 foot = 0.3048 meters.)(Round your answer to the nearest dollar.)
Solution
First, we need to convert the dimensions of the sandbox from feet to meters, since the cost of sand is given per cubic meter.
1 foot = 0.3048 meters
So,
Length = 11 feet = 11 * 0.3048 = 3.35 meters (approximately) Width = 8 feet = 8 * 0.3048 = 2.44 meters (approximately) Depth = 2 feet = 2 * 0.3048 = 0.61 meters (approximately)
Next, we calculate the volume of the sandbox in cubic meters. The volume of a rectangular prism (which is the shape of the sandbox) is given by the formula:
Volume = Length * Width * Depth
So,
Volume = 3.35 meters * 2.44 meters * 0.61 meters = 5 cubic meters (approximately)
Finally, we calculate the cost of the sand. The cost of sand is $30 per cubic meter, so the total cost is:
Cost = Volume * Cost per cubic meter
Cost = 5 cubic meters * 150
So, it will cost Andrea approximately $150 to purchase sand for the sandbox.
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