Question

cassandras work
total volume = v of prism - v of pyramid
= bh - bh
= (7)(6)(7) - (7)(6)(3)
= 294 - 126
= 168 square inches
what mistakes did cassandra make? choose three correct answers
she subtracted the
pyramid volume
instead of adding it.
she used square units
instead of cubic units.
she should have
multiplied the
dimensions of the
prism by 1/3.
she incorrectly
identified the shapes
composing the total
figure.
in calculating the
volume of the pyramid,
she did not multiply by
1/3

Explanation:

• Volume units: Volume is measured in cubic units, not square units. Square units are for area.
• Pyramid volume formula: The volume of a pyramid is \(V=\frac{1}{3}Bh\). Cassandra did not multiply by \(\frac{1}{3}\) when calculating the pyramid's volume.
• Correct operation: There is no indication that the total volume should be prism volume minus pyramid volume. But if we assume the formula \(V = V_{prism}-V_{pyramid}\) is correct for the composite - shape (which is a valid approach for some composite - shapes made by removing a pyramid from a prism), the main formula - related mistakes are in the unit and the pyramid - volume calculation.

Answer:

She used square units instead of cubic units. ; She should have multiplied the dimensions of the pyramid (in the volume formula) by \(\frac{1}{3}\) (i.e., in calculating the volume of the pyramid, she did not multiply by \(\frac{1}{3}\)).