Ten identical lengths of wire are laid closely side by side. Their combined width is measured and found to be 14.2 mm. Calculate:
a)the radius of a single wire
b)the volume in mm cubed of a single wire if its length is 10.0 cm. (Volume of a cylinder = π*radius squared*height).
diameter of each is 1.42 mm, so
radius = 0.71 mm
I'm sure you can get the volume now.
1) Ten identical lengths of wire are laid closely side-by-side. Their combined width is measured and found to be 14.2mm. Calculate:
a) the radius of a single wire
b) the volume in mm3 of a single wire if its length is 10.0 cm. (Volume of cylinder = (pie)r^2,where r=radius and h=height
158.43 mm^3
A:::the width is same as diameter so we first divide it by 10 and the by 2 to find the radius because by dividing by 10 you found the width same a diameter and then to find a radius you have to multiply by two
B:::now you have the radius and the length same as height so you use the formula like::(have to convert cm into mm)
(pie)0.71*0.71multiply100=158.33mm^3
To find the radius of a single wire:
Step 1: Determine the total width of all the wires combined.
In this case, the total width is given as 14.2 mm.
Step 2: Calculate the width of a single wire.
Since there are ten identical wires laid side by side, the width of a single wire can be obtained by dividing the total width by the number of wires.
Width of a single wire = Total width / Number of wires = 14.2 mm / 10 = 1.42 mm.
Step 3: Find the radius of the wire.
The width of a wire represents the diameter. To get the radius, divide the diameter by 2.
Radius of a single wire = Width of a single wire / 2 = 1.42 mm / 2 = 0.71 mm.
Therefore, the radius of a single wire is 0.71 mm.
To find the volume of a single wire if its length is 10.0 cm:
Step 1: Convert the length to millimeters.
As the radius and width are in millimeters, we need to convert the length to millimeters as well. Since there are 10 mm in 1 cm, the length in millimeters is 10.0 cm * 10 mm/cm = 100 mm.
Step 2: Use the volume formula for a cylinder.
The volume of a cylinder is given by the formula V = π * (radius^2) * height.
Step 3: Calculate the volume.
Using the given radius of 0.71 mm and the converted length of 100 mm in the formula, we can calculate the volume.
Volume of a single wire = π * (0.71 mm)^2 * 100 mm = π * (0.71 mm)^2 * 100 mm^3.
Step 4: Evaluate the expression.
The final step is evaluating the expression using a calculator.
Volume of a single wire ≈ 3.14159 * (0.71 mm)^2 * 100 mm^3.
Therefore, the volume of a single wire is approximately equal to 157.9085 mm^3.