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Kipish [7]
3 years ago
15

Kenji packed an exercise ball into a cylindrical package . How much space does the package occupy in terms of pi . Enter your an

swer in the box . The height of the package is 5 feet and the radius os 3 feet
Mathematics
1 answer:
grandymaker [24]3 years ago
3 0

Answer:

The space that the package would occupy is 45\pi cubic feet.

Step-by-step explanation:

The space that the package occupies is the volume of the cylinder. The volume of an object is the 3 dimensional capacity of the object.

Volume of a cylinder = \pir^{2}h

where: r is the radius and h is the height of the cylinder.

Given that; h = 5 feet and r = 3 feet.

The required volume = \pi × (3)^{2} × 5

                                   = \pi  × 9 × 5

                                  = 45\pi cubic feet

The space that the package would occupy is 45\pi cubic feet.

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zmey [24]
Alrighty


squaer base so length=width, nice


v=lwh
but in this case, l=w, so replace l with w
V=w²h

and volume is 32000
32000=w²h


the amount of materials is the surface area
note that there is no top
so
SA=LW+2H(L+W)
L=W so
SA=W²+2H(2W)
SA=W²+4HW

alrighty

we gots
SA=W²+4HW and
32000=W²H

we want to minimize the square foottage
get rid of one of the variables
32000=W²H
solve for H
32000/W²=H
subsitute

SA=W²+4WH
SA=W²+4W(32000/W²)
SA=W²+128000/W

take derivitive to find the minimum
dSA/dW=2W-128000/W²
where does it equal 0?

0=2W-1280000/W²
128000/W²=2W
128000=2W³
64000=W³
40=W

so sub back
32000/W²=H
32000/(40)²=H
32000/(1600)=H
20=H

the box is 20cm height and the width and length are 40cm
7 0
3 years ago
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