You are pouring the concrete foundation for your new office

You are pouring the concrete foundation for your new office. The office space 27 feet by 18 feet and the foundation will be 8 inches thick, if concrete cost$70 cubic yard. How much will it cost to pour the foundation?

Solution

13)

Foundation

length = 27 feet

Width = 18 feet

Height = h feet (assumed as foundation height is not given)

Volume of the foundation = 27*18*h = 486h Cubic Feet

Thickness of concrete = 8 inches = 8/12 = 2/3 feet

Volume of concrete length wise = (27*2/3)h + (27*2/3)h = 36h

For calculating widthwise volume we need to deduct 2*2/3 = 4/3ft from width

The effective width = 18 - 4/3 = 50/3

The volume of concrete widthwise = ((50/3)*(2/3))h + ((50/3)*(2/3))h = (200/3)h

Total concrete volume = (200/9)h + 36h

= h((200/9) + 36) = (524/9)h cubic feet

1 yard = 3feet

1 cubic yard = 3*3*3 = 27 cubic feet

or

1 cubic feet = 1/27 cubic yard

Concrete volume in Cubic Yards = (524/9)h*(1/27) = 524h/243 = 2.16h cubic yards

cost of 1 cubic yard = $70

Cost of 2.16h cubic yards = 2.16h*70 = $151.2h

So the cost varies with the height of foundation

14)

Express 12,509,000 in scientific notation

= 1.2509*10⁷