Answers:
- 13. volume = 452.42 cubic centimeters
- 14. volume = 2778.37 cubic inches
- 15. They need 1134.12 square inches of rubber.
Each value is approximate.
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Step-by-step explanation:
For each question I'll use my calculator's stored value of pi to get the most accuracy possible. If your teacher requires you to use something like pi = 3.14 instead, then be sure to follow such instructions.
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Problem 13
Use the circumference C = 37.7 to find the radius r.
C = 2*pi*r
37.7 = 2*pi*r
r = 37.7/(2pi)
r = 6.000141 approximately.
Then we can find the volume of a full sphere of this radius.
V = (4/3)*pi*r^3
V = (4/3)*pi*(6.000141)^3
V = 904.842473 approximately
Split this in half to get a hemispherical volume.
904.842473/2 = 452.4212365
That then rounds to 452.42 cubic centimeters.
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Problem 14
The cube has side lengths 18 inches.
Half of which is 18/2 = 9 inches. This is the radius of the sphere.
Let's find the volume of the sphere.
V = (4/3)*pi*r^3
V = (4/3)*pi*9^3
V = 3053.628059 approximately
Then we subtract this from the volume of the cube (18^3 = 5832)
5832 - 3053.628059 = 2778.371941 = 2778.37 cubic inches
This is the approximate amount of space not taken up by the sphere. It's the volume of the surrounding foam.
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Problem 15
d = diameter = 9.5
r = radius
r = d/2 = 9.5/2 = 4.75
SA = surface area of a sphere
SA = 4pi*r^2
SA = 4pi*(4.75)^2
SA = 283.528737
One basketball will need approximately 283.528737 square inches of rubber to cover the surface.
Four identically sized basketballs, of the same exact material, will need about 4*283.528737 = 1134.114948 = 1134.12 square inches of rubber.
This is the approximate minimum amount of rubber needed. The manufacturer should order more rubber because some of that material is likely going to be wasted.