ch pyramid has a greater volume and how much greater is its volu 8 in. 4 in. 6 in. 9 in. 8 in. 10 in. The volume of the pyramid on the left is greater by 8 in.3. The volume of the pyramid on the left is greater by 24 in.3. The volume of the pyramid on the right is greater by 8 in.3. The volume of the pyramid on the right is greater by 24 in.3.
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Given: Length = 8 in, Width = 6 in, Height = 8 in Volume = (8 * 6 * 8) / 3 = 128 in^3 Show more…
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Volume of the Great Pyramid Refer to the formula and the discussion in Exercise 107 . (a) Use $V=\frac{1}{3} h\left(a^{2}+a b+b^{2}\right)$ to determine a formula for the volume of a pyramid with square base of length $b$ and height $h$ by letting $a=0$ (b) The Great Pyramid in Egypt had a square base of length $756 \mathrm{ft}$ and a height of 481 ft. Find the volume of the Great Pyramid to the nearest tenth million cubic feet. Compare it with the 273 -ft-tall Superdome in New Orleans, which has an approximate volume of 100 million $\mathrm{ft}^{3}$. (Source: Guinness Book of World Records.) (c) The Superdome covers an area of 13 acres. How many acres, to the nearest tenth, does the Great Pyramid cover? (Hint: 1 acre $=43,560 \mathrm{ft}^{2}$ )
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Volume of the Great Pyramid An amazing formula from ancient mathematics was used by the Egyptians to find the volume of the frustum of a square pyramid, as shown in the figure. Its volume is given by $$ V=\frac{1}{3} h\left(a^{2}+a b+b^{2}\right) $$ where $b$ is the length of the base, $a$ is the length of the top, and $h$ is the height. (Data from Freebury, H. A., A History of Mathematics, Macmillan Company, New York. (a) When the Great Pyramid in Egypt was partially completed to a height $h$ of $200 \mathrm{ft}$, $b$ was $756 \mathrm{ft},$ and $a$ was $314 \mathrm{ft} .$ Calculate its volume at this stage of construction to the nearest thousand feet. (b) Try to visualize the figure if $a=b$. What is the resulting shape? Find its volume. (c) Let $a=b$ in the Egyptian formula and simplify. Are the results the same?
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