Question

what is the volume of this pyramid? 945 cm³ 1260 cm³ 1890 cm³ 2520 cm³

Explanation:

Step1: Find the area of the base (right triangle)

The base is a right triangle with legs 14 cm and 18 cm. The area of a right triangle is $\frac{1}{2} \times \text{base} \times \text{height}$. So, area of base $= \frac{1}{2} \times 14 \times 18$.
Calculating: $\frac{1}{2} \times 14 \times 18 = 7 \times 18 = 126$ $cm^2$.

Step2: Use the pyramid volume formula

The volume of a pyramid is $V = \frac{1}{3} \times \text{base area} \times \text{height of pyramid}$. The height of the pyramid is 30 cm.
So, $V = \frac{1}{3} \times 126 \times 30$.
Calculating: $\frac{1}{3} \times 126 \times 30 = 42 \times 30 = 1260$ $cm^3$.

Answer:

1260 $cm^3$ (corresponding to the option "1260 $cm^3$")