Here are the step-by-step solutions for each problem on the worksheet. Remember, to find the volume of any prism or cylinder, you generally multiply the
Area of the Base by the
Height (or length) of the shape.
1) Rectangular Prism
*
Formula: Volume = Length × Width × Height
*
Calculation: $5 \text{ yd} \times 2 \text{ yd} \times 12 \text{ yd}$
* $5 \times 2 = 10$
* $10 \times 12 = 120$
*
Volume: 120 cubic yards
2) Triangular Prism
*
Step 1: Find the area of the triangular base.
* Formula: $\frac{1}{2} \times \text{base} \times \text{height}$
* Calculation: $\frac{1}{2} \times 14 \text{ in} \times 3 \text{ in} = 7 \times 3 = 21 \text{ sq in}$
*
Step 2: Multiply by the length of the prism.
* Calculation: $21 \text{ sq in} \times 10 \text{ in} = 210$
*
Volume: 210 cubic inches
3) Trapezoidal Prism
*
Step 1: Find the area of the trapezoid base.
* Formula: $\frac{1}{2} \times (\text{base}_1 + \text{base}_2) \times \text{height}$
* Calculation: $\frac{1}{2} \times (11 \text{ ft} + 19 \text{ ft}) \times 7 \text{ ft}$
* $11 + 19 = 30$
* $\frac{1}{2} \times 30 = 15$
* $15 \times 7 = 105 \text{ sq ft}$
*
Step 2: Multiply by the length of the prism.
* Calculation: $105 \text{ sq ft} \times 8 \text{ ft} = 840$
*
Volume: 840 cubic feet
4) Parallelogram Prism
*
Step 1: Find the area of the parallelogram base.
* Formula: $\text{base} \times \text{height}$
* Calculation: $13 \text{ ft} \times 6 \text{ ft} = 78 \text{ sq ft}$
*
Step 2: Multiply by the length of the prism.
* Calculation: $78 \text{ sq ft} \times 4 \text{ ft} = 312$
*
Volume: 312 cubic feet
5) Cylinder
*
Formula: Volume = $\pi \times r^2 \times h$
*
Given: Radius ($r$) = 8 yd, Height ($h$) = 16 yd, $\pi = 3.14$
*
Calculation:
* $r^2 = 8 \times 8 = 64$
* $3.14 \times 64 = 200.96$
* $200.96 \times 16 = 3215.36$
*
Volume: 3,215.36 cubic yards
6) Rectangular Prism
*
Formula: Volume = Length × Width × Height
*
Calculation: $15 \text{ in} \times 9 \text{ in} \times 9 \text{ in}$
* $9 \times 9 = 81$
* $15 \times 81 = 1215$
*
Volume: 1,215 cubic inches
7) Word Problem: Rectangular Prism
*
Given: Length = 17 ft, Width = 3 ft, Height = 21 ft
*
Calculation: $17 \times 3 \times 21$
* $17 \times 3 = 51$
* $51 \times 21 = 1071$
*
Volume: 1,071 cubic feet
8) Word Problem: Parallelogram Prism
*
Step 1: Find the area of the base (parallelogram).
* Base = 25 in, Height of base = 7 in
* Area = $25 \times 7 = 175 \text{ sq in}$
*
Step 2: Multiply by the length of the prism.
* Length = 12 in
* Volume = $175 \times 12$
* $175 \times 12 = 2100$
*
Volume: 2,100 cubic inches
Final Answer:
1) 120 cu yd
2) 210 cu in
3) 840 cu ft
4) 312 cu ft
5) 3,215.36 cu yd
6) 1,215 cu in
7) 1,071 cu ft
8) 2,100 cu in
Parent Tip: Review the logic above to help your child master the concept of volume of prisms and cylinders worksheet answers.
