Question

1)
volume =
2)
volume =
3)
volume =

1. length = 9 in ; width = 7 in ; height = 5 in
2. width = 1 ft ; height = 20 ft ; length = 5 ft

Explanation:

The formula for the volume of a rectangular pyramid is $V = \frac{1}{3} \times l \times w \times h$, where $l$ = base length, $w$ = base width, $h$ = pyramid height.

1) Step1: Identify given values

$l=18$ in, $w=12$ in, $h=19$ in

1) Step2: Substitute into volume formula

$V = \frac{1}{3} \times 18 \times 12 \times 19$
$V = 6 \times 12 \times 19 = 72 \times 19 = 1368$
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2) Step1: Identify given values

$l=10$ ft, $w=4$ ft, $h=8$ ft

2) Step2: Substitute into volume formula

$V = \frac{1}{3} \times 10 \times 4 \times 8$
$V = \frac{1}{3} \times 320 = \frac{320}{3} \approx 106.67$
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3) Step1: Identify given values

$l=14$ yd, $w=6$ yd, $h=13$ yd

3) Step2: Substitute into volume formula

$V = \frac{1}{3} \times 14 \times 6 \times 13$
$V = 14 \times 2 \times 13 = 28 \times 13 = 364$
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4) Step1: Identify given values

$l=9$ in, $w=7$ in, $h=5$ in

4) Step2: Substitute into volume formula

$V = \frac{1}{3} \times 9 \times 7 \times 5$
$V = 3 \times 7 \times 5 = 105$
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5) Step1: Identify given values

$l=5$ ft, $w=1$ ft, $h=20$ ft

5) Step2: Substitute into volume formula

$V = \frac{1}{3} \times 5 \times 1 \times 20$
$V = \frac{100}{3} \approx 33.33$

Answer:

1. $1368$ cubic inches
2. $\frac{320}{3}$ cubic feet (or approximately $106.67$ cubic feet)
3. $364$ cubic yards
4. $105$ cubic inches
5. $\frac{100}{3}$ cubic feet (or approximately $33.33$ cubic feet)