Volume of a Pyramid Worksheets - Free Printable

I will solve this problem by calculating the volume of each mixed pyramid shown in the image. A "mixed pyramid" typically refers to a composite shape, often a prism (or cuboid) with a pyramid on top. The total volume is the sum of the volume of the base prism and the volume of the pyramid.

The formulas I'll use are:
- Volume of a rectangular prism = length × width × height
- Volume of a pyramid = (1/3) × base area × height

I will go through each problem one by one.

Problem 1

- Base: Rectangular prism with dimensions 12 yd × 12 yd × 12 yd
- Top: Pyramid with base 12 yd × 12 yd and height 17 yd

Volume of prism = 12 × 12 × 12 = 1728 yd³
Volume of pyramid = (1/3) × (12 × 12) × 17 = (1/3) × 144 × 17 = 816 yd³
Total volume = 1728 + 816 = 2544.00 yd³

Problem 2

- Base: Rectangular prism with dimensions 16 ft × 16 ft × 7 ft
- Top: Pyramid with base 16 ft × 16 ft and height 19 ft

Volume of prism = 16 × 16 × 7 = 1792 ft³
Volume of pyramid = (1/3) × (16 × 16) × 19 = (1/3) × 256 × 19 ≈ 1621.33 ft³
Total volume = 1792 + 1621.33 = 3413.33 ft³

Problem 3

- This appears to be a triangular pyramid (tetrahedron) with a triangular base.
- Base: Triangle with base 10 in and height 13 in
- Height of pyramid: 11 in

Area of triangular base = (1/2) × 10 × 13 = 65 in²
Volume of pyramid = (1/3) × 65 × 11 ≈ 238.33 in³

Problem 4

- This appears to be a triangular pyramid with a right triangular base.
- Base: Right triangle with legs 3 in and 5 in
- Height of pyramid: 8 in

Area of triangular base = (1/2) × 3 × 5 = 7.5 in²
Volume of pyramid = (1/3) × 7.5 × 8 = 20.00 in³

Problem 5

- Base: Rectangular prism with dimensions 7 yd × 7 yd × 4 yd
- Top: Pyramid with base 7 yd × 7 yd and height 9 yd

Volume of prism = 7 × 7 × 4 = 196 yd³
Volume of pyramid = (1/3) × (7 × 7) × 9 = (1/3) × 49 × 9 = 147 yd³
Total volume = 196 + 147 = 343.00 yd³

Problem 6

- Base: Rectangular prism with dimensions 13 ft × 8 ft × 8 ft
- Top: Pyramid with base 13 ft × 8 ft and height 15 ft

Volume of prism = 13 × 8 × 8 = 832 ft³
Volume of pyramid = (1/3) × (13 × 8) × 15 = (1/3) × 104 × 15 = 520 ft³
Total volume = 832 + 520 = 1352.00 ft³

Problem 7

- This appears to be a triangular pyramid with a triangular base.
- Base: Triangle with base 14 ft and height 9 ft
- Height of pyramid: 16 ft

Area of triangular base = (1/2) × 14 × 9 = 63 ft²
Volume of pyramid = (1/3) × 63 × 16 = 336.00 ft³

Problem 8

- Base: Rectangular prism with dimensions 11 in × 11 in × 11 in
- Top: Pyramid with base 11 in × 11 in and height 18 in

Volume of prism = 11 × 11 × 11 = 1331 in³
Volume of pyramid = (1/3) × (11 × 11) × 18 = (1/3) × 121 × 18 = 726 in³
Total volume = 1331 + 726 = 2057.00 in³

Problem 9

- Base: Rectangular prism with dimensions 15 yd × 8 yd × 8 yd
- Top: Pyramid with base 15 yd × 8 yd and height 17 yd

Volume of prism = 15 × 8 × 8 = 960 yd³
Volume of pyramid = (1/3) × (15 × 8) × 17 = (1/3) × 120 × 17 = 680 yd³
Total volume = 960 + 680 = 1640.00 yd³

Here are the final answers for each problem:

1) 2544.00 yd³
2) 3413.33 ft³
3) 238.33 in³
4) 20.00 in³
5) 343.00 yd³
6) 1352.00 ft³
7) 336.00 ft³
8) 2057.00 in³
9) 1640.00 yd³