the base of a rectangular prism is congruent to the base of a pyramid. The height of the pyramid is 3 times the height of the prism. Which figure has a greater volume? Explain.
I'm terrible with these kind of word problems. If you could explain that would be great.
can someone please help me!?!
ht. of rectangle = h.
ht. of pyramid = 3h.
Vr = Ab*h = Volume of rectangle.
Vp = Ab*3h/3,
The "3s" cancel.
Therefore, Vp = Vr = Ab*h.
Based on the dimensions given,the
volume of the rectangle is equal to
the volume of the pyramid.
Ab*h = Volume of pyramid
A rectangular prism has a base of 12cm2 and a height of 6 cm what is its volume
To compare the volumes of a rectangular prism and a pyramid, we need to know the formula for finding the volume of each shape.
The volume of a rectangular prism is determined by multiplying the length, width, and height of the prism. The formula is:
Volume of prism = length × width × height
The volume of a pyramid can be found by multiplying the area of the base and the height, then dividing the product by 3. The formula is:
Volume of pyramid = (base area × height) / 3
Now, let's tackle the problem step by step. We know that the base of the rectangular prism is congruent (the same) as the base of the pyramid.
Let's assume that the length of the base is 'L' and the width is 'W'. Therefore, the base area of both the prism and the pyramid would be L × W.
The height of the prism is 'H', so the height of the pyramid is 3 times that, which is 3H.
Now, we can calculate the volume of the rectangular prism using the formula: Volume of prism = L × W × H.
And the volume of the pyramid can be calculated using the formula: Volume of pyramid = (L × W × 3H) / 3.
Simplifying the formulas, we find:
Volume of prism = LWH
Volume of pyramid = (LWH) / 3
Since the base area and the height are the same for both shapes, we can see that the volume of the pyramid is one-third of the volume of the rectangular prism.
Therefore, the rectangular prism has a greater volume than the pyramid.