The Rainforest Pyramid has a height of 10 stories (approximately 10 feet per story) , and the Aquarium Pyramid has a height of 12 stories. If the base areas of the pyramids are equal, how many times bigger is the volume of the Aquarium Pyramid than of the Rainforest Pyramid? explain.
ok. so i know that v=1/3 bh.....so I made a hypothetical problem keeping the base as 1 ft...I got volume of Rainforest as 33 and volume of Aquarium as 40...but now I am stuck....help and thank you
the volume is proportional to the height
A / R = 12 / 10 ... A = 1.2 R
To find the volume of each pyramid, you correctly used the formula V = 1/3 * base area * height. Since the base areas of the pyramids are equal, we can focus on comparing the heights to determine the volume ratio.
Let's label the height of the Rainforest Pyramid as h_r and the height of the Aquarium Pyramid as h_a. We are given that h_r = 10 stories (10 ft per story) and h_a = 12 stories. Therefore, h_r = 10 * 10 = 100 ft and h_a = 12 * 10 = 120 ft.
Now we can calculate the volume of each pyramid using the formula. Since the base areas are equal, we can ignore them in our comparison, focusing only on the heights.
Volume of Rainforest Pyramid: V_r = 1/3 * base area * h_r = 1/3 * base area * 100
Volume of Aquarium Pyramid: V_a = 1/3 * base area * h_a = 1/3 * base area * 120
To compare the volume of the Aquarium Pyramid to the Rainforest Pyramid, we can compute the volume ratio as:
V_a / V_r = (1/3 * base area * 120) / (1/3 * base area * 100)
The base areas cancel out, leaving us with:
V_a / V_r = 120 / 100 = 1.2
This means that the volume of the Aquarium Pyramid is 1.2 times bigger than the volume of the Rainforest Pyramid. In other words, the Aquarium Pyramid is 20% larger in volume than the Rainforest Pyramid.