6th Grade Volume of Prisms with Fractional Edges Test Solutions and Scoring (PDF)

\(6 \cdot 4 \cdot 5 = 120\).

The volume is \(120\text{ cm}^{3}\).

Scoring: 1 point for the formula; 1 point for 120 with units.

\(\frac{5}{2} \cdot 4 \cdot 2 = 20\).

The volume is \(20\text{ ft}^{3}\).

Scoring: 1 point for the setup; 1 point for 20 cubic feet.

Cubes: \(6 \cdot 4 \cdot 2 = 48\). Each is \(\frac{1}{8}\) cubic inch.

\(48 \cdot \frac{1}{8} = 6\) cubic inches.

Scoring: 1 point for 48 cubes; 1 point for 6 cubic inches.

\(V = \frac{2}{3} \cdot 9 = 6\).

The volume is \(6\text{ m}^{3}\).

Scoring: 1 point for V = Bh; 1 point for 6.

\(60 = 5 \cdot 4 \cdot h = 20h\).

\(h = 3\).

Scoring: 1 point for the equation; 1 point for 3 inches.

\(2 \cdot \frac{3}{2} \cdot 1 = 3\).

It holds \(3\text{ ft}^{3}\).

Scoring: 1 point for the setup; 1 point for 3 cubic feet.

A: \(5 \cdot 4 \cdot 3 = 60\). B: \(6 \cdot 3 \cdot 3 = 54\).

Box A is greater by \(60 – 54 = 6\) cubic inches.

Scoring: 1 point for both volumes; 1 point for the comparison.

Bin: \(3 \cdot 2 \cdot \frac{3}{2} = 9\) cubic feet.

Cube: \(\frac{1}{8}\) cubic foot.

\(9 \div \frac{1}{8} = 72\) cubes. (Check: \(6 \cdot 4 \cdot 3 = 72\) cubes along the length, width, and height.)

Scoring: 1 point for the bin volume; 1 point for the cube volume; 1 point for 72.

\(8 \cdot 5 \cdot \frac{3}{4} = 30\) cubic feet.

Cost: \(\$4.00 \cdot 30 = \$120.00\).

Scoring: 1 point for the setup; 1 point for 30 cubic feet; 1 point for $120.