Question

the stainless steel in a solid cylindrical rod has a 1.00 inch in diameter and density of 7.75 g/cm3. if we want a 1.00 kg mass of this rod, how long a section (in cm) must we cut off?

Answer 1

To obtain a 1.00 kg mass of the stainless steel rod, a section approximately 25.90 cm long must be cut off.

Step-by-step explanation:

To find the length of the section that needs to be cut off from the stainless steel rod to obtain a 1.00 kg mass, we can use the formula:

mass = density x volume

Given that the density of the stainless steel rod is 7.75 g/cm³ and the desired mass is 1.00 kg, we can rearrange the formula to solve for the volume:

volume = mass / density

Substituting the values, we have:

volume = 1000 g / 7.75 g/cm³

Converting the volume from g to cm³:

volume = 129.03 cm³

Since the rod is cylindrical, we can use the formula for the volume of a cylinder to find its length:

volume = πr²h

Given that the diameter of the rod is 1.00 inch, we can convert it to cm by multiplying it by 2.54:

radius = 0.5 inch x 2.54 cm/inch = 1.27 cm

Substituting the values in the volume formula, we have:

129.03 cm³ = π(1.27 cm)²h

Solving for h, we get:

h = 129.03 cm³ / (π(1.27 cm)²) ≈ 25.90 cm

Therefore, to obtain a 1.00 kg mass of the stainless steel rod, a section approximately 25.90 cm long must be cut off.