Back to Explain circle area and volume formulas — Problem 4 · Task Set 33

Exercises: Informal Arguments for Volume and Area Formulas

Grade 10·24 problems·~30 min·Common Core Math - HS Geometry·standard·hsg-gmd-a-1

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Fluency Practice

$A square pyramid and a square prism with the same base B and height h, showing that three pyramids fill the prism$

A square pyramid and a square prism share the same square base (area $B$ ) and the same height $h$ . A student fills the pyramid with sand three times and pours it into the prism. The prism is exactly full. What does this demonstrate about the pyramid's volume?

$V_{\text{pyramid}} = Bh$ , the same as the prism, since both have the same base and height

$V_{\text{pyramid}} = \frac{1}{2}Bh$ , because the pyramid is half the size of the prism

$V_{\text{pyramid}} = \frac{1}{3}Bh$ , because three pyramids exactly fill one prism of the same base and height

$V_{\text{pyramid}} = \frac{1}{4}Bh$ , because the pyramid tapers to a point at the top