Convert to improper fractions: $$4\frac{1}{2} = \frac{9}{2}$$ and $$1\frac{5}{6} = \frac{11}{6}$$. Total volume = base area × height = $$\frac{9}{2} \times \frac{11}{6} = \frac{99}{12} = \frac{33}{4} = 8\frac{1}{4}$$ cubic feet. Water volume = $$\frac{3}{4} \times 8\frac{1}{4} = \frac{3}{4} \times \frac{33}{4} = \frac{99}{16} = 6\frac{3}{16}$$ cubic feet. Choice B gives the total tank volume. Choice C incorrectly adds dimensions. Choice D uses wrong fraction operations.

Convert to improper fractions: Volume = $$\frac{15}{2}$$, length = $$\frac{5}{2}$$, width = $$\frac{6}{5}$$. Using V = lwh: $$\frac{15}{2} = \frac{5}{2} \times \frac{6}{5} \times h$$. First find $$\frac{5}{2} \times \frac{6}{5} = \frac{30}{10} = 3$$. So $$\frac{15}{2} = 3h$$, which gives $$h = \frac{15}{2} \div 3 = \frac{15}{2} \times \frac{1}{3} = \frac{15}{6} = \frac{5}{2}$$ inches. Choice B repeats the length value. Choice C uses incorrect division. Choice D results from calculation errors.

First convert mixed numbers: $$3\frac{1}{2} = \frac{7}{2}$$ and $$2\frac{1}{4} = \frac{9}{4}$$. Volume = $$\frac{7}{2} \times \frac{9}{4} \times \frac{2}{3} = \frac{7 \times 9 \times 2}{2 \times 4 \times 3} = \frac{126}{24} = \frac{21}{4} = 5.25$$ cubic yards. Cost = $$5.25 \times 45 = 236.25$$. Choice B uses incorrect conversion of mixed numbers. Choice C doubles the correct volume. Choice D uses wrong dimension calculations.

This question tests calculating the volume of rectangular prisms with fractional edge lengths using V=bh, base area times height, and understanding that packing with fractional unit cubes gives the same result. Base 12 1/2 cm²=25/2 cm², height 4/5 cm, V=(25/2)×(4/5)=(25×4)/(2×5)=100/10=10 cm³. If dimensions were known, V=lwh would match. Packing: suppose base fits certain cubes, but formula directly gives 10 cm³. Units cm³. Mistake like adding 12.5 + 0.8=13.3, or multiplying wrongly to 16. Calculate: (25/2)×(4/5)=10 cm³.

This question tests calculating the volume of rectangular prisms with fractional edge lengths using V=lwh, where you multiply the three edges, and understanding that packing with fractional unit cubes yields the same result. Dimensions: 3/4 ft × 2 ft × 1 1/2 ft (convert to 3/2 ft), so V=(3/4)×2×(3/2)=(3/4)×(3/2)×2=(9/8)×2=18/8=9/4 ft³. Or base (3/4)×2=3/2 ft², times height 3/2 ft = (3/2)×(3/2)=9/4 ft³. Packing with 1/4 ft cubes: along 3/4 fits 3, 2 fits 8, 3/2 fits 6, total 3×8×6=144 cubes each (1/4)³=1/64 ft³, 144×1/64=144/64=9/4 ft³. Units ft³. Error like adding fractions wrongly to 3/4 + 2 + 3/2 = 17/4. Steps: convert mixed to improper; multiply (3/4)×2×(3/2)=9/4.

This question tests calculating the volume of rectangular prisms with fractional edge lengths using V=lwh (multiply three edges) or V=bh (base area times height), understanding packing with fractional unit cubes gives same result. Volume V=lwh: multiply length, width, height (2 ft × 3 ft × (1/2) ft = 2×3×0.5=3 ft³, fractional edges multiply like any numbers). Or V=bh: base area l×w times height (base 5×4=20 m², height 2.5 m, volume 20×2.5=50 m³). Packing: fill prism with unit cubes (if edge 1/2 ft, unit cube is (1/2)³=1/8 ft³, box 2×1×(1/2) holds 2÷(1/2)×1÷(1/2)×(1/2)÷(1/2)=4×2×1=8 cubes of 1/8 ft³ each, total 8×(1/8)=1 ft³—same as V=lwh). Units: cubic (ft³, cm³, in³—length unit cubed). For this prism, number of cubes: (2/(1/2)) × (1/(1/2)) × ((1/2)/(1/2)) = 4×2×1=8. Common errors include multiplying dimensions instead of dividing or miscounting fits.

To calculate the volume of a rectangular prism with fractional edge lengths, use the formula V = l × w × h, where you multiply the three dimensions, or V = base area × height, and understand that packing the prism with fractional unit cubes yields the same result. For example, with dimensions 2 ft × 3 ft × (1/2) ft, V = 2 × 3 × 0.5 = 3 ft³; alternatively, using base area, if the base is 5 m × 4 m = 20 m² and height 2.5 m, then V = 20 × 2.5 = 50 m³; packing with 1/2 ft cubes in a 2 × 3 × (1/2) prism holds 4 × 6 × 1 = 24 cubes, each 1/8 ft³, totaling 3 ft³, with units always in cubic form like ft³ though here it's count. Another example: a prism 2 ft × 3 ft × (1/2) ft has V = 2 × 3 × (1/2) = 3 ft³; or 2.5 cm × 4 cm × 3 cm: V = 30 cm³; or base 6 × 5 = 30 cm², height 2.5 cm, V = 75 cm³. For this prism 1 ft × (1/2) ft × (1/2) ft packed with (1/2) ft cubes, along length 1/(1/2)=2, width (1/2)/(1/2)=1, height (1/2)/(1/2)=1, so 2 × 1 × 1 = 2 cubes. Common errors include thinking volume is 1 × 0.5 × 0.5 = 0.25 then dividing wrong to 1 or 8, confusing with cube volume $(1/2)^3$=1/8 then miscounting to 4, adding, or ignoring packing. To calculate packing, divide each dimension by cube edge: 1/(0.5)=2, etc., multiply counts 2×1×1=2; relates to V / cube volume = (0.25) / (0.125) = 2. Packing verifies formula; real for storage; avoid misdividing, confusing volume with count, adding, wrong units.

To calculate the volume of a rectangular prism with fractional edge lengths, use the formula V = l × w × h, where you multiply the three dimensions, or V = base area × height, and understand that packing the prism with fractional unit cubes yields the same result. For example, with dimensions 2 ft × 3 ft × (1/2) ft, V = 2 × 3 × 0.5 = 3 ft³; alternatively, using base area, if the base is 5 m × 4 m = 20 m² and height 2.5 m, then V = 20 × 2.5 = 50 m³; packing with 1/2 ft cubes in a 2 × 3 × (1/2) prism holds 4 × 6 × 1 = 24 cubes, each 1/8 ft³, totaling 3 ft³, with units always in cubic form like cm³. Another example: a prism 2 ft × 3 ft × (1/2) ft has V = 2 × 3 × (1/2) = 3 ft³; or 2.5 cm × 4 cm × 3 cm: V = 2.5 × 4 × 3 = 30 cm³; or base 6 × 5 = 30 cm², height 2.5 cm, V = 30 × 2.5 = 75 cm³. For this science container measuring 2.5 cm × 4 cm × 3 cm, the volume is 2.5 × 4 × 3 = 30 cm³. Common errors include adding dimensions like 2.5 + 4 + 3 = 9.5, forgetting cubic units to get 30 cm², mishandling decimals such as 2.5 × 4 = 100 incorrectly, using V = l + w + h, multiplying only two like 2.5 × 4 = 10 then forgetting 3, or errors like 2.5 × 4 = 1. For calculating, identify dimensions l=2.5, w=4, h=3, multiply as 2.5 × 4 = 10 then 10 × 3 = 30, and use cm³; mixed numbers convert to decimals like 1(1/2)=1.5 for multiplication. Base-height method: find base l × w, multiply by h; packing confirms formula; real uses include storage, aquariums, rooms; avoid adding, wrong units, fraction mishaps, missing dimensions, sum formulas.

To calculate the volume of a rectangular prism with fractional edge lengths, use the formula V = l × w × h, where you multiply the three dimensions, or V = base area × height, and understand that packing the prism with fractional unit cubes yields the same result. For example, with dimensions 2 ft × 3 ft × (1/2) ft, V = 2 × 3 × 0.5 = 3 ft³; alternatively, using base area, if the base is 2 ft × 3 ft = 6 ft² and height 0.5 ft, then V = 6 × 0.5 = 3 ft³; packing with 1/2 ft cubes, the prism holds 4 along length, 6 along width, and 1 along height for 24 cubes, each 1/8 ft³, totaling 3 ft³, with units always in cubic form like ft³. Another example: a prism 2.5 cm × 4 cm × 3 cm has V = 2.5 × 4 × 3 = 30 cm³; or with base 6 cm × 5 cm = 30 cm² and height 2.5 cm, V = 30 × 2.5 = 75 cm³. For this storage box with dimensions 2 ft × 3 ft × (1/2) ft, the volume is 2 × 3 × 0.5 = 3 ft³. Common errors include adding dimensions like 2 + 3 + 0.5 = 5.5, forgetting cubic units to get 3 ft, mishandling fractions such as 2 × 3 ÷ 2 = 3 but sequenced wrong, using V = l + w + h, multiplying only two dimensions like 2 × 3 = 6, or decimal mistakes like treating 0.5 as 5. To calculate, identify the dimensions l=2, w=3, h=0.5, multiply step-by-step as 2 × 3 = 6 then 6 × 0.5 = 3, and add cubic units ft³; for mixed numbers, convert to improper fractions or decimals like 1(1/2) = 3/2 = 1.5 for easier multiplication. Using the base-height method, compute base area l × w then multiply by h; packing verifies the formula by showing the same volume; in real life, this applies to storage boxes for capacity, aquariums for water volume, or rooms for air space; avoid mistakes like adding instead of multiplying, omitting cubic units, fraction errors, forgetting the third dimension, or using sum formulas.

This question tests calculating the volume of rectangular prisms with fractional edge lengths using V=lwh (multiply three edges) or V=bh (base area times height), understanding packing with fractional unit cubes gives same result. Volume V=lwh: multiply length, width, height (3/4 ft × 4 ft × 2 ft = (3/4)×4×2=6 ft³, fractional edges multiply like any numbers). Or V=bh: base area l×w times height (base 5×4=20 m², height 2.5 m, volume 20×2.5=50 m³). Packing: fill prism with unit cubes (if edge 1/2 ft, unit cube is (1/2)³=1/8 ft³, box 2×3×(1/2) holds 2÷(1/2)×3÷(1/2)×(1/2)÷(1/2)=4×6×1=24 cubes of 1/8 ft³ each, total 24×(1/8)=3 ft³—same as V=lwh). Units: cubic (ft³, cm³, in³—length unit cubed). For this prism, V=(3/4)×4×2=3×2=6 ft³. Common errors include improper fraction multiplication or adding dimensions.