the volume of a rectangular prism is 600 in.3
, what is the volume of a rectangular
pyramid whose base and height is congruent to the prism? (1 point)
• 1,200 in. 3
O 1,800 in. 3
• 300 in. 3
• 200 in.3
The volume of a rectangular prism is given by the formula V = lwh, where l is the length, w is the width, and h is the height.
Given that the volume of the rectangular prism is 600 in^3, we know that V = 600.
In a rectangular pyramid,
V = (1/3)bh
Since the base and height of the rectangular pyramid are congruent to the prism, we have the following relationships:
l = b
w = l
h = w
Therefore,
V = 600 = (1/3)(l)(l)(w)
V = 600 = (1/3)(l^2)(w)
Since w = l, we can substitute w with l in the above equation:
V = 600 = (1/3)(l^2)(l)
V = 600 = (1/3)l^3
Solving for l, we get:
l^3 = 600 * 3 = 1800
l = cubed root of 1800 ≈ 12.71
Therefore, the volume of the rectangular pyramid is given by:
V = 1/3(l^2)(l)
V ≈ 1/3(12.71^2)(12.71)
V ≈ 1/3 * 161.3 * 12.71
V ≈ 1/3 * 2050.523
V ≈ 683.5 in^3
Therefore, the volume of the rectangular pyramid whose base and height are congruent to the prism is 683.5 in^3.