A Pyramid has a height of 6cm and base edge 8cm. A similar pyramid has a height of 9cm.
If the volume of the larger pyramid is 130.5cm^3 what is the volume of the smaller pyramid?
The volume of the smaller pyramid is 64.5cm^3.
To find the volume of the smaller pyramid, we can use the concept of similar figures.
We know that the ratio of the heights of the two pyramids is 6cm/9cm, which simplifies to 2/3.
Since the pyramids are similar, the ratio of their volumes would be equal to the cube of the ratio of their corresponding lengths (or edges) because volume is a three-dimensional concept.
So, (Volume of Smaller Pyramid) / (Volume of Larger Pyramid) = (Height of Smaller Pyramid)^3 / (Height of Larger Pyramid)^3
Plugging in the given values:
(Volume of Smaller Pyramid) / 130.5 cm^3 = (2/3)^3
Simplifying the right side of the equation:
(Volume of Smaller Pyramid) / 130.5 cm^3 = (8/27)
Now, we can solve for the volume of the smaller pyramid.
(Volume of Smaller Pyramid) = (8/27) * 130.5 cm^3
Calculating the result:
(Volume of Smaller Pyramid) = 39 cm^3
Therefore, the volume of the smaller pyramid is 39 cm^3.
To find the volume of the smaller pyramid, we can use the concept of proportional volumes.
Let's assume the volume of the smaller pyramid is V2 and the volume of the larger pyramid is V1.
According to the concept of proportional volumes, the ratio of the volumes of two similar pyramids is equal to the ratio of the cubes of their corresponding dimensions.
In this case, we have the height of the smaller pyramid (h2) as 6cm and the height of the larger pyramid (h1) as 9cm. The ratio of their heights is:
h2/h1 = 6/9 = 2/3
Using the concept of proportional volumes:
V2/V1 = (h2/h1)^3 = (2/3)^3
V2/V1 = 8/27
To find the volume of the smaller pyramid (V2), we multiply the volume of the larger pyramid (V1) by the ratio we found:
V2 = V1 * (8/27)
Given that the volume of the larger pyramid (V1) is 130.5cm^3, we can substitute the value and solve for V2:
V2 = 130.5 * (8/27)
V2 ≈ 38.5 cm^3
Therefore, the volume of the smaller pyramid is approximately 38.5 cm^3.