a cylindrical metal bar has a base radius of 2cm and a height of 9cm. it is melted down and recast into a tube. Find a side of the cube
V = pi r^2 h = pi (4)(9) = 113
s^3 = 113
s = 4.84 cm
Well, well, well! It seems like we're about to do some math! Let's get rolling!
To find the side length of a cube formed from melting down the cylindrical metal bar, we need to think about the volume.
The volume of the cylinder is given by the formula V = πr²h, where "r" is the base radius and "h" is the height. So, plugging in the values we have, we get V = π(2cm)²(9cm) = 36π cm³.
Since we know that the cylinder is melted down and recast into a cube, the volume of the cube will be the same as that of the cylinder. Therefore, the volume of the cube is also 36π cm³.
Now, to find the side length "s" of the cube, we can use the formula V = s³, where "V" is the volume and "s" is the side length.
So, we have 36π cm³ = s³. To isolate "s", we can take the cube root of both sides: s = ∛(36π cm³).
Now, the cube root of 36 is... well, guess what? It's 3! And, my dear friend, the cube root of π (pi) is just π (pi) itself.
Therefore, the side length of the cube is s = 3π cm. Voila! There you have it!
To find the side of the cube that can be formed from the cylindrical metal bar, we need to calculate the volume of the cylindrical bar and then find the side length of a cube with an equal volume.
Step 1: Calculate the volume of the cylindrical bar.
The formula for the volume of a cylinder is V = πr^2h, where "r" is the radius of the base and "h" is the height of the cylinder.
Given:
Base radius (r) = 2 cm
Height (h) = 9 cm
Using the formula, the volume (V) of the cylindrical bar is:
V = π(2^2)(9) = 36π cm^3
Step 2: Find the side length of the cube with the same volume.
The volume of a cube is given by the formula V = s^3, where "s" is the side length of the cube.
Setting the volume of the cube equal to the volume of the cylindrical bar, we have:
s^3 = 36π
To find the side length (s):
s = ∛(36π)
Now, you can use a calculator to find the approximate value of ∛(36π) or keep it as the exact value.
Therefore, the side length of the cube that can be formed from the cylindrical metal bar is ∛(36π) (or its approximate equivalent).
To find the side of the cube, we need to determine the volume of the cylindrical bar and then calculate the side length of a cube with the same volume.
1. Volume of the cylindrical bar:
The formula to calculate the volume of a cylinder is V = π * r^2 * h, where V represents the volume, π is a mathematical constant approximately equal to 3.14, r is the base radius, and h is the height of the cylinder.
In this case, the base radius (r) is 2 cm, and the height (h) is 9 cm. Therefore, the volume (V) of the cylindrical bar can be calculated as follows:
V = π * (2 cm)^2 * 9 cm
2. Cube side length:
The formula to calculate the volume of a cube is V = s^3, where V represents the volume and s is the side length of the cube.
We can equate the volume of the cube with the volume of the cylindrical bar to find the side length of the cube.
So, s^3 = V
Now, substitute the value of V that we determined from the cylindrical bar and solve for s:
s^3 = π * (2 cm)^2 * 9 cm
Taking the cube root of both sides will give us the side length (s) of the cube:
s = ∛[π * (2 cm)^2 * 9 cm]
Using a calculator, evaluate this expression to find the approximate value of s.