I'm having trouble with a physics question in the book (no answer given)?

Question

Could you please help me derive the answer.

The base of a pyramid covers an area of 13.0 acres (1 acre = 43,560 ft2) and has a height of 481 ft (Fig. P1.24). If the volume of a pyramid is given by the expression V = (1/3)bh, where b is the area of the base and h is the height, find the volume of this pyramid in cubic meters.

Answer 1

V = 13 * 43,560 ft^2 * 481 ft * 1/3 = 90793560 ft³

1 ft * 12 in/ft * 2.54 cm/in * 1 m/100 cm = 0.3048 m

1 ft³ = 0.028316846592 m³

90793560 ft³ * 0.028316846592 m³ /1 ft³ = 2570987 m³

Edit: Forgot the 13 on my original calc.

Answer 2

Fine...but you'll kick youreself, it's so simple.

V = .333 b h

= .333 x 13 acres x 481 ft - plug in numbers

= .333 x 13 acres x 43.560 ft^2/acres x 481 ft - convert acres to ft^2

= .333 x 13 acres x 43.560 ft^2/acres x 481 ft x (1 m^3/ (3.28)^3 ft^3) - here i used 3.28 ft is 1 m, and said 1 m^3, acubic meter is 3.28^3 ft^3

Now multiply all the numbers and all the units should cancel out except for - cubic meters or m^3, that you volume of the pyramid.

Hope that helps

Answer 3

b = (13)(43,560ft²)

b = 566,280ft²

V = 1/3(566,280ft²)(481ft)

V = 90,793,560ft³

1ft³ = .02832m³

V = (90,793,560)(.02832m³)

V = 2,571,273.619m³