There is a rectangular prisim And pyra.I'd with congruent bases and heights If the volume of the pyramid is 48in What is the volume of the prisim
Since the prism and the pyramid have congruent bases and heights, their volumes are proportional.
The volume of the pyramid is given as 48 in³. Let's denote the volume of the prism as V.
Since the volume of the pyramid is 1/3 of the volume of the prism (since they both have the same base and height), we have:
V(prism) = 3 * V(pyramid)
V(prism) = 3 * 48
V(prism) = 144 in³
Therefore, the volume of the prism is 144 in³.
A rectangular prison has A base Area of 15 And pyramid with congruent base and height Has volume of 20 What is height of Rectangular prisim
To find the height of the rectangular prism, we need to use the known volumes of the pyramid and prism as well as the base area of the prism.
Let the height of the prism be denoted as h.
The volume of the pyramid is given as 20. Since the prism and pyramid have congruent bases and heights, the volume of the prism is 3 times the volume of the pyramid:
V_prism = 3 * V_pyramid
V_prism = 3 * 20
V_prism = 60
The base area of the prism is given as 15, so the volume of the prism can also be expressed as:
V_prism = base area * height
60 = 15 * h
h = 60 / 15
h = 4
Therefore, the height of the rectangular prism is 4 units.
The base is 6 and the height is 9 for the triangular pyramid and prison what is the volume of Rach shape
To find the volumes of the pyramid and prism with a base of 6 and a height of 9, we can use the formulas for the volume of a prism and a pyramid.
For the prism:
Volume_Prism = base area * height
Volume_Prism = 6 * 9
Volume_Prism = 54
So, the volume of the prism is 54 cubic units.
For the pyramid:
Volume_Pyramid = (1/3) * base area * height
Volume_Pyramid = (1/3) * 6 * 9
Volume_Pyramid = 18
So, the volume of the pyramid is 18 cubic units.
The options are
72 216
216 72
108 36
36 108
To clarify, the volume of the prism is 54 cubic units and the volume of the pyramid is 18 cubic units.
The correct set of options doesn't seem to match the calculated volumes. Let's examine the options further:
A. 72, 216
The sum of these values is 72 + 216 = 288, which is not equal to the volume of the prism or the pyramid.
B. 216, 72
The sum of these values is 216 + 72 = 288, which is not equal to the volume of the prism or the pyramid.
C. 108, 36
The sum of these values is 108 + 36 = 144, which is also not equal to the volume of the prism or the pyramid.
D. 36, 108
The sum of these values is 36 + 108 = 144, which is not equal to the volume of the prism or the pyramid.
Based on the calculated volumes of the prism and the pyramid (54 and 18 cubic units, respectively), none of the provided options match the correct values.