Stewart has a rectangular prism that has a volume of 96 cubic inches. Rohan has a cube that measure 8 inches on each side. Rohan thinks his cube has a greater volume than Stewart’s cube. Is Rohan correct and how do you know?
You are wrong,
You do 8x8x8 and it equals 512.
So Rohan is correct
ah, ok sorry. like i said, been a while since i did volume so i forgot if i multiply 8*8*8 or if its 8*8 but nice job helping
To determine if Rohan's cube has a greater volume than Stewart's rectangular prism, we need to compare their volumes.
Volume of Stewart's rectangular prism:
Since we know that the volume of a rectangular prism is given by the formula V = length x width x height, and Stewart's rectangular prism has a volume of 96 cubic inches, we can use this information to solve for the dimensions.
Let's assume the dimensions of Stewart's rectangular prism are length (L), width (W), and height (H).
Therefore, we have the equation L x W x H = 96.
Now, we need to find all possible combinations of three positive integers whose product is 96.
The possible combinations of three positive integers whose product is 96 are:
1 x 1 x 96
1 x 2 x 48
1 x 3 x 32
1 x 4 x 24
1 x 6 x 16
1 x 8 x 12
2 x 2 x 24
2 x 3 x 16
2 x 4 x 12
2 x 6 x 8
3 x 4 x 8
Notice that in each combination, the product is 96.
However, since we're comparing volumes, we need to find which combination yields the greatest volume. To do this, we compare the dimensions in each combination.
By examining the combinations, we can see that the combination with the largest dimensions that satisfies the equation is 4 x 4 x 6. So, Stewart's rectangular prism has dimensions of 4 inches by 4 inches by 6 inches.
Now let's calculate the volume of Rohan's cube.
Volume of Rohan's cube:
Since a cube has all sides equal in length, we can calculate the volume of Rohan's cube using the formula V = side length^3.
Given that Rohan's cube has a side length of 8 inches, we can plug this value into the formula: V = 8^3 = 512 cubic inches.
Comparing the volumes:
Comparing the volumes, we found that Stewart's rectangular prism has a volume of 96 cubic inches, while Rohan's cube has a volume of 512 cubic inches.
Therefore, Rohan is incorrect in assuming that his cube has a greater volume than Stewart's rectangular prism.