Question

p30. a pyramid has a height of 481 ft, and its base covers area of 13.0 acres. the volume of a pyramid is given by the expression ( v = \frac{1}{3} b h ) where b is the area of the base and h is the height. find the volume of this pyramid in cubic meters, given that 1 acre = 43,560 ( \text{ft}^2 ).

Explanation:

Step1: Convert acres to square feet

$B = 13.0 \text{ acres} \times 43560 \frac{\text{ft}^2}{\text{acre}} = 566280 \text{ ft}^2$

Step2: Calculate volume in cubic feet

$V = \frac{1}{3}Bh = \frac{1}{3} \times 566280 \text{ ft}^2 \times 481 \text{ ft} = 90792360 \text{ ft}^3$

Step3: Convert cubic feet to cubic meters

(Use $1 \text{ ft} = 0.3048 \text{ m}$, so $1 \text{ ft}^3 = (0.3048)^3 \text{ m}^3$)
$V = 90792360 \text{ ft}^3 \times (0.3048)^3 \frac{\text{m}^3}{\text{ft}^3} \approx 90792360 \times 0.0283168 \text{ m}^3$

Answer:

$\approx 2.57 \times 10^6 \text{ cubic meters}$ (or $2570000 \text{ m}^3$ rounded to a reasonable precision)