Expressions, Equations, and Relationships>Solving Problems with Volumes of Prisms and Pyramids(TEKS.Math.7.9.A)
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Texas 7th Grade Math › Expressions, Equations, and Relationships>Solving Problems with Volumes of Prisms and Pyramids(TEKS.Math.7.9.A)
A triangular prism has a triangular base with base 9 cm and height 8 cm. The length of the prism is 12 cm. What is the volume?
864 cm³
432 cm³
144 cm³
54 cm³
Explanation
Prisms use $V = Bh$, where $B$ is the area of the base. The base is a triangle, so $B = \tfrac{1}{2}bh = \tfrac{1}{2}\cdot 9\cdot 8 = 36,\text{cm}^2$. Then $V = Bh = 36\cdot 12 = 432,\text{cm}^3$. Distractors: $864$ (forgot $\tfrac{1}{2}$), $144$ (incorrectly divided by 3 as if a pyramid), $54$ (used wrong dimensions).
A rectangular pyramid has a base length of 10 m, base width of 6 m, and a height of 9 m. What is the volume?
540 m³
90 m³
270 m³
180 m³
Explanation
Pyramids use $V = \tfrac{1}{3}Bh$. For a rectangular base, $B = lw = 10\cdot 6 = 60,\text{m}^2$. Then $V = \tfrac{1}{3}\cdot 60\cdot 9 = \tfrac{1}{3}\cdot 540 = 180,\text{m}^3$. Distractors: $540$ (used prism formula), $90$ (wrong factor), $270$ (mixed-up computation).
A triangular pyramid has a base area of 45 cm² and a height of 12 cm. What is the volume?
180 cm³
540 cm³
90 cm³
270 cm³
Explanation
For a pyramid, use $V = \tfrac{1}{3}Bh$. Here $B = 45,\text{cm}^2$ and $h = 12,\text{cm}$. So $V = \tfrac{1}{3}\cdot 45\cdot 12 = 15\cdot 12 = 180,\text{cm}^3$. Remember: prisms use $V=Bh$ while pyramids use $V=\tfrac{1}{3}Bh$.
Which formula should be used to find the volume of a triangular prism?
$V=\frac{1}{3}lwh$
$V=Bh$
$V=lwh$
$V=\frac{1}{3}Bh$
Explanation
Prisms use $V = Bh$, where $B$ is the area of the base. For a triangular prism, $B=\tfrac{1}{2}bh$ of the triangle, then multiply by the prism's length/height. Formulas with $\tfrac{1}{3}$ are for pyramids, not prisms.