Which of the following square pyramids have a volume of 24 mm. choose all that apply
a square pyramid with a side length of 9 mm and a height of 8 mm
a square pyramid with a side length of 3 mm and a height of 8 mm
a square pyramid with a side length of 2 mm and a height of 18 mm
a square pyramid with a side length of 6 mm and a height of 4 mm
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To find the volume of a square pyramid, you can use the formula:
Volume = (1/3) * base area * height
where the base area is the area of the square at the base of the pyramid.
Let's calculate the volume for each given square pyramid and see which ones have a volume of 24 mm.
1. Square pyramid with a side length of 9 mm and a height of 8 mm:
Base area = (9 mm)^2 = 81 mm^2
Volume = (1/3) * 81 mm^2 * 8 mm = 216 mm^3
2. Square pyramid with a side length of 3 mm and a height of 8 mm:
Base area = (3 mm)^2 = 9 mm^2
Volume = (1/3) * 9 mm^2 * 8 mm = 24 mm^3
3. Square pyramid with a side length of 2 mm and a height of 18 mm:
Base area = (2 mm)^2 = 4 mm^2
Volume = (1/3) * 4 mm^2 * 18 mm = 24 mm^3
4. Square pyramid with a side length of 6 mm and a height of 4 mm:
Base area = (6 mm)^2 = 36 mm^2
Volume = (1/3) * 36 mm^2 * 4 mm = 48 mm^3
So, the square pyramids with a volume of 24 mm are:
- a square pyramid with a side length of 3 mm and a height of 8 mm
- a square pyramid with a side length of 2 mm and a height of 18 mm