Question

plaese help me!


a physical education teacher was getting ready for gym class one day. he measured the circumference of the basketball to be 9 inches when its filled with air. he then went on to pose the following questions to his classes:

A) how much material is needed to make four basketball? (3.14 for pie)

Answer 1

b) how much air will the four balls hold combined? ( 3.14 for pie)

Answer 2

c) if the basketballs are stored four to a box in cubic boxes whose edges are 15 incges long, what percent of the box is not filled by balls?

Answer 3

part a), you're finding the surface area of the ball or sphere

Answer 4

do you know the formula for the surface area of a sphere?

Answer 5

yes

Answer 6

ok what is it

Answer 7

well first off, you'll need to find the radius before you can find the surface area

Answer 8

4(3.14)r squared

Answer 9

C = 2*pi*r

9 = 2*3.14*r

solve for r

Answer 10

good, keep that formula in mind for later

Answer 11

okay the problem u just out up is for A right?

Answer 12

yes

Answer 13

r=4.5

Answer 14

9 = 2*3.14*r

9/(2*3.14) = r

1.43312 = r

r = 1.43312

Answer 15

now you use this in

4(3.14)r squared

to find the surface area

Answer 16

i got 25.796 for surface area

Answer 17

good

Answer 18

that was for B right??

Answer 19

now multiply that answer by 4

why? because that answer of 25.796 is the surface area of one basketball

but you want to make 4 basketballs

Answer 20

no all still on part a

Answer 21

103.184

Answer 22

that's your final answer to part a

Answer 23

that's how much material you need to make the four basketballs

Answer 24

yes i got that

Answer 25

for part B do i use Volume?

Answer 26

yes you use the formula

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

Answer 27

that's to get the volume of one ball

Answer 28

i got 49.2916 for 4 balls

Answer 29

very good

Answer 30

getting the same pretty much

Answer 31

so the volume of 4 balls is roughly 49.2916 cubic inches

Answer 32

yes :) i don't get what i have to do for part C??

Answer 33

what is the volume of the box?

Answer 34

i don't know

Answer 35

V = s^3

V = 15^3

V = 3375 cubic inches

Answer 36

okay i got it :)
i have one last question :)

Answer 37

well we're not done with C, do you see how to get the answer for C?

Answer 38

using what I gave you

Answer 39

what do i do next ??

Answer 40

the volume of the four balls was 49.2916

Answer 41

the volume of the box is 3375

Answer 42

so the volume inside the box that is NOT taken up by the 4 balls is

3375 - 49.2916 = 3325.7084

Answer 43

therefore, the percent of the box NOT filled by the balls is

3325.7084/3375 = 0.985395 = 98.5395%

Answer 44

so you have a lot of room in this box

Answer 45

got it :)

Answer 46

the school would like to sane money ans storage space by buying smaller boxes to store the balls. what is the smallest size for the box where it will still hold four balls and each edge will be a whole number/

Answer 47

last question :)

Answer 48

ok say the box had side lengths of 1 inch

this would give it a volume of 1^3 = 1 cubic inches

that's too small since we need something that will hold 49.2916 cubic inches

Answer 49

2^3 = 8 ... still too small

3^3 = 27 ... again too small

4^3 = 64 ... not too small

Answer 50

so the smallest box has side lengths of 4 inches

Answer 51

thank you soo much :)

Answer 52

sure thing