Question

The base of a pyramid covers an area of 13.0 acres (1 acre = 43,560 ft2) and has a height of 481 ft. 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

Answer:

2570987.31 m³

Explanation:

Base area = 13 acres = b

Converting to ft²

1 acre = 43,560 ft²

⇒13 acre = 566280 ft²

Height of pyramid = 481 ft = h

Volume

$v=\frac{1}{3}bh\\\Rightarrow v=\frac{1}{3}566280\times 481\\\Rightarrow v=90793560\ ft^3$

Converting to cubic meters

1 ft = 0.3048 m

⇒1 ft³ = 0.3048×0.3048×0.3048 m³

⇒1 ft³ =  0.3048³ m³

90793560 ft³ = 90793560×0.3048³

⇒90793560 ft³ = 2570987.31 m³

∴ Volume of this pyramid is 2570987.31 m³

Answer 2

V = 1/3 Bh v = 1/3 (13 ac)(43560ft^2/ac)(481ft) v = 90793560 ft^3 * 0.3048m/ft * 0.3048m/ft * 0.3048m/ft = 2570987m^3