To find the volume of a pyramid, we use the formula:
[tex]\[ \text{Volume} = \frac{1}{3} \times \text{Base Area} \times \text{Height} \][/tex]
In this case, the base of the pyramid is a rectangle with length [tex]\( l = 10 \)[/tex] cm and width [tex]\( w = 18 \)[/tex] cm. The height [tex]\( h \)[/tex] of the pyramid is 12 cm.
First, calculate the area of the base (which is a rectangle):
[tex]\[ \text{Base Area} = l \times w \][/tex]
[tex]\[ \text{Base Area} = 10 \, \text{cm} \times 18 \, \text{cm} \][/tex]
[tex]\[ \text{Base Area} = 180 \, \text{cm}^2 \][/tex]
Next, use the formula for the volume of a pyramid:
[tex]\[ \text{Volume} = \frac{1}{3} \times \text{Base Area} \times \text{Height} \][/tex]
[tex]\[ \text{Volume} = \frac{1}{3} \times 180 \, \text{cm}^2 \times 12 \, \text{cm} \][/tex]
Now, perform the multiplication:
[tex]\[ \text{Volume} = \frac{1}{3} \times 2160 \, \text{cm}^3 \][/tex]
[tex]\[ \text{Volume} = 720 \, \text{cm}^3 \][/tex]
So, the volume of the pyramid is:
[tex]\[ 720 \, \text{cm}^3 \][/tex]
Thus, the correct answer is:
○ 720 cm³
