Answer:
≈ 416.755 cm³
Explanation:
To find the volume of the rectangular pyramid OABCD, you can use the formula:
Volume = (1/3) × Base Area × Height
First, calculate the base area. Since ABCD is a rectangle, its area is given by the product of its length (AB) and width (BC):
Base Area = AB × BC
= 20 cm × 18 cm
= 360 cm²
Next, calculate the height of the pyramid. In triangle AOC, you have angle AOC given as 100 degrees and side AC (which is the height of the pyramid). Since AO and OC are equal due to the symmetry of the rectangle pyramid, you can use the trigonometric function cosine to find AC:
Cosine (θ) = Adjacent / Hypotenuse
Cosine (100°) = AC / AO
AC = AO × Cosine (100°)
Since AO = AB = 20 cm:
AC = 20 cm × Cosine (100°)
Now, calculate the value of Cosine (100°). Keep in mind that trigonometric functions usually take angles in radians, so you'll need to convert degrees to radians:
Cosine (100°) = Cosine (100 × π / 180) ≈ -0.173648
Multiply this value by 20 cm to find AC:
AC ≈ -0.173648 × 20 cm ≈ -3.47296 cm
The negative value arises because the angle is obtuse, and cosine is negative in the second quadrant.
Since the height of the pyramid can't be negative, take the absolute value of AC:
AC = 3.47296 cm
Finally, use the formula for the volume of the pyramid:
Volume = (1/3) × Base Area × Height
= (1/3) × 360 cm² × 3.47296 cm
≈ 416.755 cm³