How does the volume of a square pyramid change if the base area is quadrupled and the height is reduced to 1/9 of its original size?
A. V= 1/27Bh
B. V= 4/27Bh
C. V= 2/9Bh
D. V= 4/9Bh
V = (1/3)base area * height
new V =(1/3) (4 base area)(height/9)
so 4/9 of original
the answer is B v=4/27Bh
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that isn't correct
How does the volume of a rectangular prism change if the width is reduced to of its original size, the height is reduced to of its original size, and the length is reduced to of its original size?
To determine how the volume of a square pyramid changes when the base area is quadrupled and the height is reduced to 1/9 of its original size, we need to understand the formula for the volume of a square pyramid and then analyze the effects of the given changes.
The formula for the volume of a square pyramid is V = (1/3) * B * h, where V represents the volume, B represents the base area, and h represents the height.
First, let's consider how the base area changes. If the base area is quadrupled, it means it becomes four times its original size. Thus, we can write the new base area as 4B.
Next, let's consider how the height changes. If the height is reduced to 1/9 of its original size, it means it becomes one-ninth of its original value. So, we can write the new height as (1/9)h.
Now, let's substitute these new values into the volume formula: V = (1/3) * (4B) * (1/9h).
Simplifying this equation, we get: V = 4/27 * Bh.
Therefore, the volume of the square pyramid, with the given changes, is V = 4/27Bh.
Hence, the correct answer is option B. V = 4/27Bh