To find the volume of the larger pyramid, we first need to find the ratio of the volumes of the two pyramids. Since volume is proportional to the cube of the linear dimension, we can set up the following equation:
(Volume of Larger Pyramid) / (Volume of Smaller Pyramid) = (Linear dimension of Larger Pyramid / Linear dimension of Smaller Pyramid)^3
Let x be the linear dimension of the larger pyramid:
(x^3) / (1^3) = 36 / 25
x^3 = 36 * 1
x = 3
Therefore, the linear dimension of the larger pyramid is 3 times the linear dimension of the smaller pyramid. Since volume is proportional to the cube of the linear dimension, the volume of the larger pyramid is (3^3) = 27 times the volume of the smaller pyramid.
If the volume of the smaller pyramid is 250m^3, then the volume of the larger pyramid is:
27 * 250 = 6750m^3
Therefore, the volume of the larger pyramid is 6750m^3.
The closest answer choice is 640m^3, so the correct answer is:
640 m3.
Two pyramids are similar with a ratio of surface areas of 25:36. Find the volume of the larger pyramid given that the first has a volume of 250m3.
97.7 m3
432 m3
640 m3
61 m3
1 answer