Volume of rubber

[phillygurl]

I have tried this and it doesn't seem right?

The volume of rubber in the hollow ball used in racquetball is modeled by the formula,
V = 4/3 iiR^3 - 4/3 iir^3

a) rewrite the formula by factoring the right hand side completely

V = 4/3 iiR^3 - 4/3iir^3
= 4/3 ii - 4/3 ii
= R^3 - r^3
V = R^3 - r^3

b) determine the value of V when R = 3cm and r = 1.5cm
V = 4/3ii(3)^3 - 4/3ii(1.5)^3
= 4/3ii(3 x 3 x 3 = 27) - 4/3ii(1.5 x 1.5 x 1.5 = 3.375)
= 4/3ii x 27/1 = 36 - 4/3ii x 3.375/1 = 4.5
= 36 - 4.5
= 31.5
V = 31.5cm

 

[wjm11]

The volume of rubber in the hollow ball used in racquetball is modeled by the formula,
V = 4/3 iiR^3 - 4/3 iir^3

a) rewrite the formula by factoring the right hand side completely

V = 4/3 iiR^3 - 4/3iir^3
= 4/3 ii - 4/3 ii
= R^3 - r^3
V = R^3 - r^3

When we factor, we are not getting rid of/canceling anything. The common factors to the two terms on the right side of the equation are (4pi/3), so if we extract these factors, we can rewrite the equation as

V = (4pi/3)(R^3 – r^3)

Notice that if we were two reverse what we have just done (factoring) by multiplying it back out (distributing), we’d end up back where we started. We must always be able to do that after we’ve factored. The factored terms do not just disappear.

 

[wjm11]

b) determine the value of V when R = 3cm and r = 1.5cm
V = 4/3ii(3)^3 - 4/3ii(1.5)^3
= 4/3ii(3 x 3 x 3 = 27) - 4/3ii(1.5 x 1.5 x 1.5 = 3.375)
= 4/3ii x 27/1 = 36 - 4/3ii x 3.375/1 = 4.5
= 36 - 4.5
= 31.5
V = 31.5cm

Your first two lines were okay, then things went wrong in the third line. Let’s use the factored form to evaluate this:

V = (4pi/3)(R^3 – r^3)
V = (4pi/3)(3^3 – 1.5^3)
V = (4pi/3)(27 - 3.375)
V = (4pi/3)(23.625)
V = 98.96 cm^3 (approx.)

 

[phillygurl]

okay okay...so when we are rewriting I am to extract the common factor in this case was 4pi/3 than times it by the remaining equation. Okay I think I am good on that - thank you!

And then on the second part - if I had wrote the problem correctly I wouldn't have divided the 3 into 27 giving me 9 then times it by 4 which gave me the 36 and I did the same for 3.375 dividing 3 into that giving me 1.5 than times it by 4 which gave me 4.5

I then took 36 - 4.5 to get 31.5

I times the two expressions and then I take he ^3 (from the original equation is brought down to the end)?

Okay I think I am good on that also - thank you!

 

[wjm11]

b) determine the value of V when R = 3cm and r = 1.5cm
V = 4/3ii(3)^3 - 4/3ii(1.5)^3
= 4/3ii(3 x 3 x 3 = 27) - 4/3ii(1.5 x 1.5 x 1.5 = 3.375)
= 4/3ii x 27/1 = 36 - 4/3ii x 3.375/1 = 4.5
= 36 - 4.5
= 31.5
V = 31.5cm

It looks as if you just lost your pi term between the third and 4th lines. Let me rewrite your third line and take it from there:

V = 4/3ii x 27/1 = 36 - 4/3ii x 3.375/1 = 4.5
V = (pi)(36) – (pi)(4.5)
V = (pi)(31.5)
V = 98.96 cm^3

Notice that your answer must have units of cm^3.

 

[phillygurl]

okay - so I can do it that way but just remember to take my answer and use the pi mode on my calculator to get the final answer. Okay - thanks again.