Prisms Volume
1. Find the volume of a rectangular prism with length 17 ft, width 3 ft, and height 21 ft.
The formula for the volume of a rectangular prism is:
$$V = \text{length} \times \text{width} \times \text{height}$$
Calculate:
$$V = 17 \times 3 \times 21 = 1071\, \text{ft}^3$$
2. Find the volume of a prism with a parallelogram base having base 25 in and height 7 in, and prism length 12 in.
Volume formula for prism:
$$V = \text{area of base} \times \text{length}$$
Calculate area of parallelogram base:
$$\text{Area} = \text{base} \times \text{height} = 25 \times 7 = 175\, \text{in}^2$$
Calculate volume:
$$V = 175 \times 12 = 2100\, \text{in}^3$$
3. Rectangular prism with sides 5 yd, 12 yd, 2 yd volume:
$$V = 5 \times 12 \times 2 = 120\, \text{yd}^3$$
4. Rectangular prism with sides 14 in, 3 in, 10 in volume:
$$V = 14 \times 3 \times 10 = 420\, \text{in}^3$$
5. Trapezoidal prism with bases 6 ft and 10 ft, height 7 ft, length 19 ft volume:
Area of trapezoid base:
$$A = \frac{(b_1 + b_2)}{2} \times h = \frac{(6 + 10)}{2} \times 7 = 56\, \text{ft}^2$$
Volume:
$$V = A \times \text{length} = 56 \times 19 = 1064\, \text{ft}^3$$
6. Parallelogram prism with base 13 ft, height 6 ft, length 4 ft volume:
Base area:
$$A = 13 \times 6 = 78\, \text{ft}^2$$
Volume:
$$V = 78 \times 4 = 312\, \text{ft}^3$$
7. Cylinder with radius 8 yd and height 16 yd volume (use \(\pi = 3.14\)):
Formula:
$$V = \pi r^2 h$$
Calculate:
$$V = 3.14 \times 8^2 \times 16 = 3.14 \times 64 \times 16 = 3215.04\, \text{yd}^3$$
8. Rectangular prism with sides 9 in, 9 in, 15 in volume:
$$V = 9 \times 9 \times 15 = 1215\, \text{in}^3$$