A solid metal cylinder has diameter 60cm and height 28cm.It is melted and recast to 50 equal cubes.Find the edge of each cube to 3 significant figures
V = πr^2h
Once you find the volume of the cylinder, divide by 50 to get the volume of each cube. The edge of each cube will be the square root of the cube volume.
I'll let you do the calculations.
actually, each edge will be the cube root of the volume.
I stand corrected. Thanks.
To find the edge length of each cube, we need to determine the volume of the metal cylinder and then divide it by the number of cubes.
Step 1: Calculate the volume of the metal cylinder.
The volume of a cylinder can be found using the formula: V = πr^2h
where V is the volume, π is a mathematical constant (approximately 3.14159), r is the radius of the cylinder, and h is the height of the cylinder.
Given that the diameter of the cylinder is 60 cm, we can find the radius by dividing it by 2.
Radius (r) = Diameter / 2
r = 60 cm / 2 = 30 cm
Now, we substitute the values into the formula to calculate the volume:
V = 3.14159 * (30 cm)^2 * 28 cm
V ≈ 79170.681 cm^3
Step 2: Determine the edge length of each cube.
To find the edge length of each cube, we need to divide the volume of the metal cylinder by the number of cubes.
Number of cubes = 50
Edge length (L) = (Volume of cylinder)^(1/3) / (Number of cubes)^(1/3)
Substituting the values, we get:
L ≈ (79170.681 cm^3)^(1/3) / (50)^(1/3)
Using a calculator, evaluate the expression:
L ≈ 17.83 cm
Therefore, the edge length of each cube, rounded to three significant figures, is approximately 17.8 cm.