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Sagot :

Problem 9

r+h = 9

SA = 2*pi*r^2 + 2*pi*r*h = 54pi

2*pi*r^2 + 2*pi*r*h = 54pi

2pi*r(r + h) = 54pi

r(r+h) = 27

r(9) = 27

9r = 27

r = 27/9

r = 3

r+h = 9

h = 9-r

h = 9-3

h = 6

Answers:  r = 3 and h = 6 are the radius and height respectively.

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Problem 10

d = diameter = 68 mm

r = radius = d/2 = 68/2 = 34 mm

SA = surface area of a sphere

SA = 4*pi*r^2

SA = 4*pi*34^2

SA = 4264pi

Answer:  4264pi square mm

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Problem 11

Plug V = 3000 into the sphere volume formula and isolate r.

V = (4/3)pi*r^3

3000 = (4/3)pi*r^3

(4/3)pi*r^3 = 3000

4pi*r^3 = 3*3000

4pi*r^3 = 9000

r^3 = 9000/(4pi)

r = cube root(  9000/(4pi)  )

r = ( 9000/(4pi) )^(1/3)

r = 8.947002 approximately

Now we can determine the surface area of this sphere.

SA = 4pi*r^2

SA = 4*pi*( 8.947002 )^2

SA = 1005.923451

Answer:  1005.923451 square feet approximately

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Problem 12

We'll follow the same idea as problem 11, but in reverse.

SA = 4*pi*r^2

400pi = 4pi*r^2

r^2 = (400pi)/(4pi)

r^2 = 100

r = sqrt(100)

r = 10

Luckily we get a nice whole number for the radius r. Use it to find the volume.

V = (4/3)*pi*r^3

V = (4/3)*pi*10^3

V = (4000/3)pi

Answer:   (4000/3)pi   cubic inches exactly

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Problem 13

The diagram is missing. I don't have enough info to be able to answer.