The Great Pyramid of Giza is a square pyramid where the length of a side of the base is 230.4 m and the height of the pyramid is 138.8 m. The pharaoh has instructed you to design a new pyramid with the same volume but with a rectangular base that is 250 m long and 150 m wide. What is the height of the new pyramid? Round your answer to the nearest tenth of a meter.
159.9 m
175.9 m
196.5 m
199.6 m
well, pointy things with straight sides tend to have volume = (1/3) base area * height
so
(1/3)(230)(230)(138.8) = (1/3)(250)(150) ( h )
typo - forgot .4
(1/3)(230.4)(230.4)(138.8) = (1/3)(250)(150) ( h )
To find the height of the new pyramid, we can use the formula for the volume of a pyramid: V = (1/3) * base area * height.
First, let's find the volume of the original pyramid.
V_original = (1/3) * (230.4m)^2 * 138.8m
Now, let's find the volume of the new pyramid.
V_new = (1/3) * (250m) * (150m) * height_new
Since the volume of the new pyramid is equal to the volume of the original pyramid, we can set up the following equation:
(1/3) * (230.4m)^2 * 138.8m = (1/3) * (250m) * (150m) * height_new
Now, let's solve for height_new:
(1/3) * (230.4m)^2 * 138.8m = (1/3) * (250m) * (150m) * height_new
Using a calculator:
height_new = ((1/3) * (230.4m)^2 * 138.8m) / ((1/3) * (250m) * (150m))
height_new ≈ 199.6m
So, the height of the new pyramid is approximately 199.6m. Round your answer to the nearest tenth of a meter.
Therefore, the correct answer is 199.6 m.
To find the height of the new pyramid, we need to first calculate the volume of the Great Pyramid of Giza.
The volume of a pyramid can be calculated using the formula:
Volume = (1/3) * base area * height
In this case, the base area can be calculated by squaring the length of one side of the base:
Base area = (230.4 m)^2
Next, we can substitute the known values into the volume formula:
Volume = (1/3) * (230.4 m)^2 * 138.8 m
Now, we can calculate the volume.
Once we have the volume of the Great Pyramid of Giza, we can use it to find the height of the new pyramid. Since the volume of the new pyramid should be the same, we can set up an equation:
(1/3) * base area * height of the new pyramid = Volume of the Great Pyramid of Giza
We know the base area of the new pyramid, which is given as 250 m * 150 m.
Now we can rearrange the equation to solve for the height of the new pyramid:
height of the new pyramid = (Volume of the Great Pyramid of Giza) / [(1/3) * base area]
Substituting the known values, we have:
height of the new pyramid = (Volume of the Great Pyramid of Giza) / [(1/3) * (250 m * 150 m)]
Now we can plug in the calculated volume of the Great Pyramid of Giza and solve for the height of the new pyramid:
height of the new pyramid = (Volume of the Great Pyramid of Giza) / [(1/3) * (250 m * 150 m)]
height of the new pyramid ≈ 199.6 m
Therefore, the height of the new pyramid would be approximately 199.6 m.