The Transamerica Pyramid is a skyscraper in San Francisco. The rectangular base has a length of 175 feet and a width of 120 feet. The height is 853 feet. Find the volume of the bui... The Transamerica Pyramid is a skyscraper in San Francisco. The rectangular base has a length of 175 feet and a width of 120 feet. The height is 853 feet. Find the volume of the building.
Understand the Problem
The question asks to calculate the volume of the Transamerica Pyramid, given that it's a pyramid-shaped building with a rectangular base of length 175 feet, a width of 120 feet and a height of 853 feet. The volume of a pyramid formula is V = (1/3) * base area * height. The base area is given by length * width.
Answer
$5,971,000$ cubic feet
Answer for screen readers
$5,971,000$ cubic feet
Steps to Solve
- Calculate the area of the rectangular base
To find the area of the rectangular base, multiply the length and width. $$ Area = length \times width = 175 \times 120 $$
- Calculate the product
$$ 175 \times 120 = 21000 $$ So, the area of the base is 21000 square feet.
- Calculate the volume of the pyramid
To find the volume of the pyramid, use the formula $V = \frac{1}{3} \times baseArea \times height$. $$ V = \frac{1}{3} \times 21000 \times 853 $$
- Calculate the product
$$ V = \frac{1}{3} \times 17913000 $$
- Divide by 3
$$ V = 5971000 $$ So, the volume of the Transamerica Pyramid is 5,971,000 cubic feet.
$5,971,000$ cubic feet
More Information
The Transamerica Pyramid is an iconic skyscraper in San Francisco, completed in 1972. While the calculation gives us its volume, the building also houses office spaces and has a unique architectural design.
Tips
A common mistake is forgetting to multiply by $\frac{1}{3}$ when calculating the volume of a pyramid. Remember that the volume of a pyramid is one-third of the base area times the height. Another common mistake is calculating the area incorrectly by using the incorrect values or not understanding the given dimensions. Always double-check to make sure your calculation of the area is accurate before proceeding with the volume calculation.
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