Question

volume of composite figures
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 \\( \frac { 1 } { 3 } \\).
she incorrectly
identified the shapes
composing the total
figure.
in calculating the
volume of the pyramid,
she did not multiply by
\\( \frac { 1 } { 3 } \\).

Explanation:

• Volume Units: Volume is measured in cubic units. Cassandra used square units (for area) instead of cubic units.
• Prism Volume: The formula for the volume of a prism is \(V = Bh\) (no \(\frac{1}{3}\) factor). She wrongly thought of multiplying prism dimensions by \(\frac{1}{3}\).
• Pyramid Volume: The formula for the volume of a pyramid is \(V=\frac{1}{3}Bh\). She did not multiply by \(\frac{1}{3}\) when calculating the pyramid's volume.

Answer:

• She used square units instead of cubic units.
• She should have multiplied the dimensions of the prism by \(\frac{1}{3}\). (This is incorrect for the prism, but it's about her wrong operation).
• In calculating the volume of the pyramid, she did not multiply by \(\frac{1}{3}\).