Measurement and Geometry

1. (a) Convert pounds to ounces:

$3 \text{ pounds} \times 16 \frac{\text{ounces}}{\text{pound}} = 48 \text{ ounces}$

The recipe needs $\mathbf{48}$ ounces of chicken.

(b) Divide the total ounces by the package size:

$48 \div 20 = 2 \text{ remainder } 8$

Two packages give only $40$ ounces, which is not enough. You must buy $\mathbf{3}$ packages ($60$ ounces) to have at least $48$ ounces.

2. (a) Volume of a rectangular prism: $V = l \times w \times h$

$V = 2 \times 1.5 \times 2 = 6 \text{ cubic feet}$

The volume of one box is $\mathbf{6}$ cubic feet.

(b) First, find the volume of the storage space:

$V_{\text{storage}} = 6 \times 3 \times 4 = 72 \text{ cubic feet}$

Then divide by the volume of one box:

$72 \div 6 = 12$

$\mathbf{12}$ boxes can fit in the storage unit.

3. (a) Volume of the water: $V = l \times w \times h$

$V = 30 \times 12 \times 20 = 7{,}200 \text{ cubic centimeters}$

(b) Convert cubic centimeters to liters:

$7{,}200 \text{ mL} = \frac{7{,}200}{1{,}000} = 7.2 \text{ liters}$

The tank holds $\mathbf{7.2}$ liters of water.

4. (a) The four points form a rectangle (all angles are $90°$ and opposite sides are equal).

(b) Side $AB$ goes from $(1, 1)$ to $(1, 5)$. The $x$-coordinates are the same, so the length is the difference in $y$-coordinates:

$|5 - 1| = 4 \text{ units}$

(c) Side $BC$ goes from $(1, 5)$ to $(4, 5)$. The $y$-coordinates are the same, so the length is the difference in $x$-coordinates:

$|4 - 1| = 3 \text{ units}$

(d) Area of a rectangle: $A = \text{length} \times \text{width}$

$A = 4 \times 3 = \mathbf{12} \text{ square units}$

5. (a) Convert yards to feet:

$100 \text{ yards} \times 3 \frac{\text{feet}}{\text{yard}} = 300 \text{ feet}$

(b) Convert feet to inches:

$300 \text{ feet} \times 12 \frac{\text{inches}}{\text{foot}} = 3{,}600 \text{ inches}$

(c) Convert $50$ yards to feet:

$50 \times 3 = \mathbf{150} \text{ feet}$