Since the rectangular pyramid and rectangular prism have congruent bases and heights, their volumes are proportional.
The volume of the rectangular pyramid is 10 cm^3.
Let the volume of the rectangular prism be V.
Since the two shapes are proportional, we can set up a proportion to find the volume of the rectangular prism:
10 cm^3 / V = (1/3)
Cross multiply:
V = 10 * 3
V = 30 cm^3
Therefore, the volume of the rectangular prism is 30 cm^3.
A rectangular pyramid has a volume of 10 cm3. What is the volume of a rectangular prism given it has a congruent base and height to the pyramid? answer pleses
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a prism and pyramid have congruent triangular bases if their height are both 15 m what is the volume of each shape
(14 m 7 m 8 m 16 m)
the volume f the prism is __ m3
the volume of the pyramid is __ m3
(14 m 7 m 8 m 16 m)
the volume f the prism is __ m3
the volume of the pyramid is __ m3
To calculate the volumes of the prism and pyramid, we first need to find the area of the congruent triangular bases.
Given the sides of the triangular base are 14 m, 7 m, and 8 m, we can calculate the area of the triangle.
Using Heron's formula:
The semiperimeter s = (14 + 7 + 8) / 2 = 29/2 = 14.5
Area = √(s(s-a)(s-b)(s-c))
Area = √(14.5(14.5-14)(14.5-7)(14.5-8))
Area = √(14.5 * 0.5 * 7.5 * 6.5)
Area = √2826.875
Area ≈ 53.18 m^2
Since the height of the prism and pyramid is 15 m, we can now calculate the volumes:
Volume of the prism = base area * height
Volume of the prism = 53.18 * 15
Volume of the prism = 797.7 m^3
Volume of the pyramid = (1/3) * base area * height
Volume of the pyramid = (1/3) * 53.18 * 15
Volume of the pyramid = (1/3) * 797.7
Volume of the pyramid ≈ 265.9 m^3
Therefore, the volume of the prism is approximately 797.7 m^3 and the volume of the pyramid is approximately 265.9 m^3.
Given the sides of the triangular base are 14 m, 7 m, and 8 m, we can calculate the area of the triangle.
Using Heron's formula:
The semiperimeter s = (14 + 7 + 8) / 2 = 29/2 = 14.5
Area = √(s(s-a)(s-b)(s-c))
Area = √(14.5(14.5-14)(14.5-7)(14.5-8))
Area = √(14.5 * 0.5 * 7.5 * 6.5)
Area = √2826.875
Area ≈ 53.18 m^2
Since the height of the prism and pyramid is 15 m, we can now calculate the volumes:
Volume of the prism = base area * height
Volume of the prism = 53.18 * 15
Volume of the prism = 797.7 m^3
Volume of the pyramid = (1/3) * base area * height
Volume of the pyramid = (1/3) * 53.18 * 15
Volume of the pyramid = (1/3) * 797.7
Volume of the pyramid ≈ 265.9 m^3
Therefore, the volume of the prism is approximately 797.7 m^3 and the volume of the pyramid is approximately 265.9 m^3.
you forgot the 16 m it’s 14 m. 7 m. 8 m. and 16 m.
Apologies for the oversight. Let's recalculate the volumes using the correct base dimensions of 14m, 7m, 8m, and 16m for the triangular bases.
First, calculate the area of the triangular base with sides 14m, 7m, and 8m. We use Heron's formula again:
Semi-perimeter = (14 + 7 + 8 + 16) / 2 = 22.5
Area = √(s(s-a)(s-b)(s-c))
Area = √(22.5(22.5-14)(22.5-7)(22.5-8))
Area = √(22.5 * 8.5 * 15.5 * 14.5)
Area = √ (22.5 * 8.5 * 15.5 * 14.5)
Area ≈ 247.37 m^2.
Now, we can calculate the volumes:
Volume of the prism = Base Area * Height = 247.37 * 15 = 3710.55 m^3.
Volume of the pyramid = (1/3) * Base Area * Height = (1/3) * 247.37 * 15 ≈ 1235.18 m^3.
Therefore, the volume of the prism is approximately 3710.55 m^3, and the volume of the pyramid is approximately 1235.18 m^3.
First, calculate the area of the triangular base with sides 14m, 7m, and 8m. We use Heron's formula again:
Semi-perimeter = (14 + 7 + 8 + 16) / 2 = 22.5
Area = √(s(s-a)(s-b)(s-c))
Area = √(22.5(22.5-14)(22.5-7)(22.5-8))
Area = √(22.5 * 8.5 * 15.5 * 14.5)
Area = √ (22.5 * 8.5 * 15.5 * 14.5)
Area ≈ 247.37 m^2.
Now, we can calculate the volumes:
Volume of the prism = Base Area * Height = 247.37 * 15 = 3710.55 m^3.
Volume of the pyramid = (1/3) * Base Area * Height = (1/3) * 247.37 * 15 ≈ 1235.18 m^3.
Therefore, the volume of the prism is approximately 3710.55 m^3, and the volume of the pyramid is approximately 1235.18 m^3.
wrong!
Let's recalculate the volumes using the correct base dimensions (14m, 7m, 8m, and 16m) for the triangular bases.
Calculate the area of the triangular base with sides 14m, 7m, 8m, and 16m using Heron's formula:
Semi-perimeter: s = (14 + 7 + 8 + 16) / 2 = 45/2 = 22.5
Area = √(s(s-a)(s-b)(s-c))
Area = √(22.5(22.5-14)(22.5-7)(22.5-8))
Area = √(22.5 * 8.5 * 15.5 * 14.5)
Area ≈ √(4571.875)
Area ≈ 67.6 m^2
Now, we can calculate the volumes:
Volume of the prism = Base Area * Height = 67.6 * 15 = 1014 m^3
Volume of the pyramid = (1/3) * Base Area * Height = (1/3) * 67.6 * 15 ≈ 337.8 m^3
Therefore, the volume of the prism is approximately 1014 m^3, and the volume of the pyramid is approximately 337.8 m^3.
Calculate the area of the triangular base with sides 14m, 7m, 8m, and 16m using Heron's formula:
Semi-perimeter: s = (14 + 7 + 8 + 16) / 2 = 45/2 = 22.5
Area = √(s(s-a)(s-b)(s-c))
Area = √(22.5(22.5-14)(22.5-7)(22.5-8))
Area = √(22.5 * 8.5 * 15.5 * 14.5)
Area ≈ √(4571.875)
Area ≈ 67.6 m^2
Now, we can calculate the volumes:
Volume of the prism = Base Area * Height = 67.6 * 15 = 1014 m^3
Volume of the pyramid = (1/3) * Base Area * Height = (1/3) * 67.6 * 15 ≈ 337.8 m^3
Therefore, the volume of the prism is approximately 1014 m^3, and the volume of the pyramid is approximately 337.8 m^3.
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