Find the ratio of the volume of two cubes whose sides are 2.6 cm and 3.4cm
The volumes of two similar objects are proportional to the cube of their sides
so vol1 : vol2 = 2.6^3 : 3.4^3
= 13^3 : 17^3
= 2197 : 4913
note: 2.6/3.4 = 26/34 = 13/17
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Ah, volume ratios, huh? Well, it's like comparing apples to oranges, or in this case, cubes to other cubes. Let's crunch the numbers, shall we?
The volume of the first cube with side length 2.6 cm is 2.6 cm * 2.6 cm * 2.6 cm = 17.576 cm³, approximately.
And the volume of the second cube with side length 3.4 cm is 3.4 cm * 3.4 cm * 3.4 cm = 39.304 cm³, give or take a smidgen.
Now, to find the ratio, we divide the volume of the second cube by the volume of the first cube. So, 39.304 cm³ ÷ 17.576 cm³ gives us... wait for it... approximately 2.231.
So, the ratio of the volumes of the two cubes is about 2.231. There you have it. But hey, who's keeping score anyway, right? Keep on cubing!
To find the ratio of the volumes of two cubes, we need to divide the volume of one cube by the volume of the other cube.
The volume of a cube is found by multiplying the length of one side by itself twice.
Let's calculate the volumes of the given cubes:
Cube 1:
Side length = 2.6 cm
Volume = (2.6 cm)^3 = 2.6 cm × 2.6 cm × 2.6 cm = 17.576 cm³
Cube 2:
Side length = 3.4 cm
Volume = (3.4 cm)^3 = 3.4 cm × 3.4 cm × 3.4 cm = 39.304 cm³
Now, let's find the ratio:
Ratio = Volume of Cube 1 / Volume of Cube 2
Ratio = 17.576 cm³ / 39.304 cm³
Simplifying the ratio:
Ratio = 0.447
Therefore, the ratio of the volume of the two cubes is approximately 0.447.
To find the ratio of the volume of two cubes, we need to calculate the volume of both cubes.
The volume of a cube is given by the formula: V = s^3, where V is the volume and s is the length of the side.
For the first cube with a side length of 2.6 cm:
V1 = (2.6 cm)^3 = 17.576 cm^3
For the second cube with a side length of 3.4 cm:
V2 = (3.4 cm)^3 = 39.304 cm^3
Now, we can find the ratio of the volumes:
Ratio = V2 / V1
Substituting the values:
Ratio = 39.304 cm^3 / 17.576 cm^3
By dividing the two volumes:
Ratio ≈ 2.23
Therefore, the ratio of the volume of the two cubes is approximately 2.23.