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.

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.

Question
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 =(1/3)bh, where b is the area of the base and his the height, find the volume of this pyramid in cubicmeters.

Answers (1)

2020-12-25
\(\displaystyle{13}\ {a}{r}{c}{e}{s}\cdot{\frac{{{43560}\ {f}{t}^{{2}}}}{{{1}\ {a}{c}{r}{e}}}}={5.66}\times{10}^{{5}}\ {f}{t}^{{2}}\)
\(\displaystyle{5.66}\times{10}^{{5}}\ {f}{t}^{{2}}\cdot{\frac{{{0.0929}\ {m}^{{2}}}}{{{1}\ {f}{t}^{{2}}}}}={5.26}\times{10}^{{4}}\ {m}^{{2}}\)
\(\displaystyle{481}{f}{t}\cdot{\frac{{{0.3048}}}{{{1}{f}{t}}}}={147}{m}\)
\(\displaystyle{V}={\frac{{{\left({5.26}\times{10}^{{4}}{m}^{{2}}{\left({147}{m}\right)}\right\rbrace}{\left\lbrace{3}\right\rbrace}={2.58}\times{10}^{{6}}{m}^{{3}}}}{}}\)
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