The volume \( V \) of a pyramid is given by the formula:
\[ V = \frac{1}{3} \times \text{Base Area} \times \text{Height} \]
For a rectangular base, the base area \( A \) is calculated as:
\[ A = \text{Length} \times \text{Width} = 7 , \text{cm} \times 9 , \text{cm} = 63 , \text{cm}^2 \]
Substituting the values into the volume formula:
\[ 231 , \text{cm}^3 = \frac{1}{3} \times 63 , \text{cm}^2 \times h \]
To isolate \( h \), first multiply both sides by 3:
\[ 693 , \text{cm}^3 = 63 , \text{cm}^2 \times h \]
Next, divide both sides by 63:
\[ h = \frac{693 , \text{cm}^3}{63 , \text{cm}^2} = 11 , \text{cm} \]
Thus, the height of the pyramid is
\[ \boxed{11 , \text{cm}} \]
1 answer