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:
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
Explanation:
Given that,
The area of the base of a pyramid, b = 43,560 ft²
The height of the pyramid, h = 481 ft
To find,
The volume of the pyramid.
Solution,
We know that,
1 ft = 0.3048 m
b = 4046.85 m² and h = 146.609 m
The volume of a pyramid is given by :
\(V=\dfrac{1}{3}bh\)
Put all the values,
\(V=\dfrac{1}{3}\times 4046.85\times 146.609\\\\V=197768.21\ m^3\)
Answer:
The volume of the pyramid is \(197768.21\ \text{feet}^3\).
Reference:
https://brainly.com/question/12630013