Question

# The base of a pyramid covers an area of 13.0 acres (1 acre =43,560 ft^2) and has a height of 481 ft . Ifthe volume of a pyramid is given by the expression V =(1/3)bh, where b is the area of the base and his the height, find the volume of this pyramid in cubicmeters.

Non-right triangles and trigonometry

The base of a pyramid covers an area of 13.0 acres (1 acre =43,560 $$\displaystyle{f}{t}^{{2}}$$) and has a height of 481 ft . Ifthe volume of a pyramid is given by the expression $$V =(\frac{1}{3})$$bh, where b is the area of the base and his the height, find the volume of this pyramid in cubicmeters.

$$\displaystyle{13}\ {a}{r}{c}{e}{s}\cdot{\frac{{{43560}\ {f}{t}^{{2}}}}{{{1}\ {a}{c}{r}{e}}}}={5.66}\times{10}^{{5}}\ {f}{t}^{{2}}$$
$$\displaystyle{5.66}\times{10}^{{5}}\ {f}{t}^{{2}}\cdot{\frac{{{0.0929}\ {m}^{{2}}}}{{{1}\ {f}{t}^{{2}}}}}={5.26}\times{10}^{{4}}\ {m}^{{2}}$$
$$\displaystyle{481}{f}{t}\cdot{\frac{{{0.3048}}}{{{1}{f}{t}}}}={147}{m}$$
$$\displaystyle{V}={\frac{{{\left({5.26}\times{10}^{{4}}{m}^{{2}}{\left({147}{m}\right)}\right\rbrace}{\left\lbrace{3}\right\rbrace}={2.58}\times{10}^{{6}}{m}^{{3}}}}{}}$$