Question

the dimensions of a square pyramid are shown in the diagram.what is the volume of the square pyramid in cubic inches?96108595127.5height of 14 cm. the base of the pyramid is shown below.what is the volume of the pyramid puzzle in cubic centimeters?1785

Explanation:

Step1: Recall pyramid volume formula

The volume $V$ of a pyramid is $V = \frac{1}{3} \times \text{Base Area} \times \text{Height}$

Step2: Solve square pyramid volume

First, calculate base area: $\text{Base Area} = 6 \times 6 = 36$ square inches.
Substitute into formula: $V = \frac{1}{3} \times 36 \times 6$
Calculate: $\frac{1}{3} \times 36 = 12$, then $12 \times 6 = 72$

Step3: Solve triangular pyramid volume

First, calculate base area (triangle): $\text{Base Area} = \frac{1}{2} \times 17 \times 15 = 127.5$ square centimeters.
Substitute into formula: $V = \frac{1}{3} \times 127.5 \times 14$
Calculate: $\frac{1}{3} \times 127.5 = 42.5$, then $42.5 \times 14 = 595$

Answer:

Volume of square pyramid: 72 cubic inches
Volume of triangular pyramid puzzle: 595 cubic centimeters