Question
11 cm height
7 cm length
10 cm width
What is the volume of the pyramid?
7 cm length
10 cm width
What is the volume of the pyramid?
Answers
Answered by
GPT 3.5
To find the volume of a pyramid, you can use the formula V = (1/3) × base area × height.
In this case, the base area is the area of the triangular base of the pyramid, which can be calculated using the formula for the area of a triangle: base × height / 2.
The height of the triangular base can be found using the Pythagorean theorem, since it is a right triangle. The height is the side perpendicular to the base, so we have:
height^2 = (11 cm)^2 - (7 cm / 2)^2
height^2 = 121 cm^2 - 24.5 cm^2
height^2 = 96.5 cm^2
height ≈ 9.823 cm
Now we can calculate the base area:
base area = (7 cm) × (9.823 cm) / 2
base area ≈ 34.7655 cm^2
Finally, we can find the volume:
V = (1/3) × 34.7655 cm^2 × 11 cm
V ≈ 128.0135 cm^3
Therefore, the volume of the pyramid is approximately 128.0135 cubic centimeters.
In this case, the base area is the area of the triangular base of the pyramid, which can be calculated using the formula for the area of a triangle: base × height / 2.
The height of the triangular base can be found using the Pythagorean theorem, since it is a right triangle. The height is the side perpendicular to the base, so we have:
height^2 = (11 cm)^2 - (7 cm / 2)^2
height^2 = 121 cm^2 - 24.5 cm^2
height^2 = 96.5 cm^2
height ≈ 9.823 cm
Now we can calculate the base area:
base area = (7 cm) × (9.823 cm) / 2
base area ≈ 34.7655 cm^2
Finally, we can find the volume:
V = (1/3) × 34.7655 cm^2 × 11 cm
V ≈ 128.0135 cm^3
Therefore, the volume of the pyramid is approximately 128.0135 cubic centimeters.