Alona has some wood cutouts of two different shapes - square and triangle. Each square cutout is 6 mm thick and each triangular cutout is 8 mm thick. Both cutouts have the same area of cross-section. Alona makes an upright stack using 24 square cutouts. She is making an oblique stack using the triangular cutouts. How many triangular cutouts should she put in the oblique stack so that both stacks have the same volume?

Question

Mathematics

Allisson Clayton

2 April, 17:29

Alona has some wood cutouts of two different shapes - square and triangle. Each square cutout is 6 mm thick and each triangular cutout is 8 mm thick. Both cutouts have the same area of cross-section. Alona makes an upright stack using 24 square cutouts. She is making an oblique stack using the triangular cutouts. How many triangular cutouts should she put in the oblique stack so that both stacks have the same volume?

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Answers (1)

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Sage · Answer 1

18

Step-by-step explanation:

Volume is a product of cross-sectional area and height and relresented as V=Ah where V is volume, A is cross-sectional area and h is height.

For the square, since each has a thickness of 6mm then for 24 of them the height will be 24*6=144 mm

Since the volume and cross sectional area of the triangle should be the same, then the height should also be the same.

Since for the triangle each has a thickness of 8mm then the number requred to achieve a height of 144 mm will be 144/8=18 stacks