Simple volume questions?

1) A copper wire is 200 metres long and has a  cross section 1.4 mm.

Calculate the volume, and also the weight when it is rolled up , at 8.8 g per cm³ 

My answer is 271.04 kg, but actual answer is 2.71 kg, so I am not seeing where I have to divide by 100.

i. e. 200,000 x 3.1416 x 0.7² = 308 m³

308 m³ = 30,800 cm³

30,800 x 8.8g = 271,040 g = 271.04 kg

2) In this question it looks like the answer in my textbook is wrong.

Two cylindrical saucepans have the same height, but the smaller pan has diameter of 15 cm and holds 1 litre of water. Calculate the diameter of the larger saucepan if it holds 2 litres.

Smaller: h x  π x 7.5² = 1,000 cm³ 

h x π =1000/56.25 =17.7777

h = 17.7777/π = 5.659 cm

Larger: 5.659 x π x r² = 2,000 cm³ 

π x r² = 2,000/5.659 = 353.419

r² = 353.419/π

r =  √ 112.497 = 10.6065

diameter of larger pan = 10.6065 x 2 = 21.21 cm

But my textbook gives an answers of 15/√2 (= 10.61). This seems a mistake in that it has given me the radius rather than the diameter, which it asked for. Or have I not seen something? Thanks.

3 Answers

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  • Anonymous
    1 month ago
    Favorite Answer

    < 200,000 x 3.1416 x 0.7² = 308 m³ >

     

    200 m = 200,000 mm.  Your equation gives you mm^3, not m^3  if you include your units IN the equation and make sure they cancel out, it's much more likely to recognize unit mistakes versus assigning units at the end.  308 m^3 is a big volume.  You should realize that 200 m of 1.4 mm diameter wire can't possibly be this much.

     

    You have 3.08 * 10^-4 m^3.  8.8 g/cm^3 = 8800 kg/m^3 = 2.71 kg

     

    For the second question, I'll use another approach to check.  We've doubled the volume, what is the new diameter?  Square root of 2 = 1.414.  This is the factor that the diameter has to increase by or 15 cm * 1.414 = 21.2 cm.  Same as you.

     

    < But my textbook gives an answers of 15/√2 (= 10.61) >

    If it's the diameter, it can't possibly be right as this is smaller than the first pot and we want to double the volume it holds for the same height.  

     

    My approach is 15 cm * √2.  If I want the radius, I divide by 2 which gives me 15 cm * √2 / 2 = 15 cm / √2 or their answer.  You are right, their answer is for the radius.

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  • Philip
    Lv 6
    1 month ago

    Length of wire = 200 m = 2*10^4 cm. I suppose by cross

    section you mean wire diameter = 1.4 mm. Then wire

    circular cross section has radius of 0.7 mm = 0.07 cm and

    wire circular cross section has area pi(0.07)^2 (cm)^2. Then volume of wire = 2pi*(10^4)(0.07)^2 (cm)^3 =

    98pi (cm)^3 = 307.8760801 (cm)^3.

    1 (cm)^3 of wire weighs 8.8 g. Therefore wire roll weighs

    2709.309504 g = 2.709309504 kg.

    For the pan problem note that volume = base area*height.

    Both pans have the same height. Larger pan holds twice

    as much as smaller pan. Therefore base area of larger pan is twice that of the smaller pan...(1). Use this fact with

    the info about the smaller pan to determine the radius of

    the larger pan.

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  • 1 month ago

    A copper wire is 200 meters long and has a  cross-section 1.4 mm

    Let's see what I get.

    Is the 1.4 mm a diameter?  Presuming it is, the radius is 0.7 mm.

    The density that we have is in cm³, so converting all lengths to cm:

    200 m (100 cm/m) = 20000 cm

    0.7 mm (1/10 cm/mm) = 0.07 cm

    Now finding the area of cross-section:

    A = πr²

    A = π(0.07)²

    A = 0.0049π cm²

    Now multiply by the length to get the volume:

    V = Al

    V = 0.0049π(20000)

    V = 98π cm³

    We have the density of 8.8 g/cm³, so multiply this density by the volume to get the weight, in grams:

    98π cm³ (8.8 g/cm³) = 862.4π g

    Conver to kg:

    862.4π g (1/1000 kg/g) = 0.8624π kg

    Using 3.14159 for π, I get:

    0.8624(3.14159) = 2.709 kg (rounded to 3DP)

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