b Divide the volume of the empty part of the aquarium by the volume of the rock from Part A.
A
a 75 cubic inches
B
b 20 rocks
Practice makes perfect
a Let's analyze the given aquarium. The aquarium is filled with water in 34.
When you submerge a rock in the aquarium, the water level rises 0.25 inch.
We are asked to find the volume of the rock. To do this, we will find the volume of the water that rises. That water is represented by the rectangular prism of dimensions 10, 30, and 0.25 inches. Its volume, V, is equal to the product of the dimensions.
V=10* 30* 0.25=75 in^3
Therefore, the volume of the rock is 75 cubic inches.
b We are asked to find how many rocks like the one in Part A can be placed in the aquarium before water spills out. First, let's find the volume of whole aquarium.
The aquarium is in the shape of a rectangular prism of dimensions 10, 20, and 30 inches. Its volume, V, is the product of the dimensions.
V=10* 20* 30=6000 in^3
Since we fill the aquarium 34 full with water, 14 of the aquarium is empty. Therefore, the volume of the non-filled part is equal to 14* 6000=1500 cubic inches. From Part A, the volume of the rock is 75 cubic inches. Therefore, we can place 150075=20 rocks in the aquarium before water spills out.
