57.4k views
4 votes
OABCD is a rectangle pyramid where AB=20cm, BC=18cm and angle AOC is 100. find the volume of pyramid

1 Answer

4 votes

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

User Ipd
by
8.5k points

Related questions

asked Jan 10, 2021 78.5k views
Vovan asked Jan 10, 2021
by Vovan
7.7k points
1 answer
2 votes
78.5k views
asked Apr 9, 2021 53.0k views
Nizar asked Apr 9, 2021
by Nizar
8.3k points
1 answer
2 votes
53.0k views
1 answer
5 votes
123k views
Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.