What is the dollar amount for the cement needed for a sidewald that is 4 inches thick, 3 feet wilde, and 40 feet long if the cement is sold for $76 petr cubic yard. Calculate the problem using fractions to avoid rounding errors caused by repeating decimals.
Convert all measures to feet and multiply.
1/3 * 3 * 40 * 3^3 * $76 = ?
$337.78
To calculate the dollar amount for the cement needed for the sidewalk, we can follow these steps:
1. Convert the measurements to the same unit. Since the cement is sold in cubic yards, we need to convert the measurements to yards.
- The sidewalk is 4 inches thick, which is equivalent to 4/36 yards (since there are 36 inches in a yard).
- The width of the sidewalk is 3 feet, which is equivalent to 3/3 yards (since 1 foot is equal to 1 yard).
- The length of the sidewalk is 40 feet, which is equivalent to 40/3 yards (since 1 yard is equal to 3 feet).
2. Calculate the volume of the sidewalk. The volume of the sidewalk is the product of its thickness, width, and length:
- Volume = (Thickness) x (Width) x (Length)
- Volume = (4/36 yards) x (3/3 yards) x (40/3 yards)
3. Simplify the fractions and calculate the volume:
- Volume = (1/9) yards x (1) yards x (40/3) yards
- Volume = (40/27) cubic yards
4. Calculate the dollar amount for the cement:
- Dollar Amount = Volume x Price per cubic yard
- Dollar Amount = (40/27) cubic yards x $76 per cubic yard
5. Simplify the fractions and calculate the dollar amount:
- Dollar Amount = (40/27) x 76 dollars
- Dollar Amount = (40 x 76)/27 dollars
- Dollar Amount ≈ $113.33 (rounded to the nearest cent)
So, the dollar amount for the cement needed for the sidewalk is approximately $113.33.