After moving into a new house a couple wants to have a concr

After moving into a new house, a couple wants to have a concrete patio poured to support a hot tub, because... well, because it\'s a hot tub. The plans call for a 14 ft by 16 ft slab of concrete 4 inches thick. round any calculations to two decimal places if you need to. How many cubic feet of concrete will be needed? Convert the volume of concrete to cubic yards. The coolest thing about ordering ready-mix concrete is that a concrete mixer will show up at your house. Most companies require orders by the cubic yard. The patio above was estimated at 3 cubic yards. How much extra concrete was ordered? Find the relative error in the estimate compared to the actual amount of concrete needed. In 2012, an average cost for concrete was $140 per cubic yard. How much would be spent on concrete for the patio at that price? Fidn the dollar value of the wasted concrete.

Solution

1. Given dimension 14ft X 16ft X4 inc = 14ft X 16ft X 1/3 ft

volume or concrete needed = (14ft)(16ft)(1/3 ft)=224/3 ft³

there volume of concrete needed= 224/3 ft³

2.since 1 ft = 1/3 yard

volume= 224/3 (1/3)³ yard³ =224/81 yard³

3.volume needed= 224/81 yard³

volume ordered =3yard³

extra orderd= 3- (224/81) = 19/81 yard³

5.Patio orderd 3 yard³ concrete

amount = 3(140) = 420 dollars

6.value of wasted concrete= 19/81 * 140= 32.84 dollars