Question

1. pyramid with 10 mi (slant height?), 8 mi (side of base), 5.2 mi (apothem?)
2. pyramid with 11 yd (height), 6 yd, 8 yd (base sides)
3. pyramid with 11 ft (height), 10 ft, 10 ft (base sides)
4. pyramid with 6 cm (height), 6 cm, 8 cm (base sides)
5. pyramid with 7 cm (height), 6 cm, 6 cm (base sides)
6. pyramid with 10 in (slant height?), 6 in (side of base), 4.1 in (apothem?)
7. triangular pyramid with 10 mi, 8 mi, 6 mi, 10 mi (edges)
8. pyramid with 8 in (height), 6 in, 6 in (base sides)
9. pyramid with 12 ft (slant height?), 6 ft (side of base), 4.1 ft (apothem?)
10. pyramid with 11 ft (slant height?), 6 ft (side of base), 5.2 ft (apothem?)

Explanation:

Let's solve for the volume of the pyramid in problem 12. The formula for the volume of a pyramid is \( V = \frac{1}{3}Bh \), where \( B \) is the area of the base and \( h \) is the height.

Step 1: Find the area of the base

The base of the pyramid in problem 12 is a square with side length \( 6 \) yd. The area of a square is \( B = s^2 \), so \( B = 6^2 = 36 \) square yards.

Step 2: Identify the height

The height \( h \) of the pyramid is given as \( 11 \) yd.

Step 3: Calculate the volume

Using the volume formula \( V = \frac{1}{3}Bh \), substitute \( B = 36 \) and \( h = 11 \):
\( V = \frac{1}{3} \times 36 \times 11 \)
First, calculate \( \frac{1}{3} \times 36 = 12 \). Then, \( 12 \times 11 = 132 \).

Answer:

The volume of the pyramid in problem 12 is \( 132 \) cubic yards.