mariasanchez47
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Would someone please help me?!

1. Explain what happens to the volume of a sphere if you double the radius.

2.A cylindrical can of tennis balls holds a stack of three balls so that they touch the can at the top, bottom, and sides. The radius of each ball is 1.25 inches. Find the volume inside the can that is not taken up by the three tennis balls.

Respuesta :

apologiabiology
1.
volume of sphere =4/3 times pi times radius^3
if radius is doubled then
4/3 times pi times (2radius)^3
what would change was from radius^3 to (2radius)^3
subsitute x for radius and solve for the difference
x^3 compared to (2x)^3
expand (2x)^3
(2x)^3=2x times 2x times 2x=8x^3
x^3 compared to 8x^3
it is 8 times larger
the volume becomes 8 times larger







2. so find:
a. volume of can
b. volume of tennis balls
then subtract b from a



a. volume of can
volume of cylnder=height times area of base
area of base=circle=pi times radius^2
volume=height times pi times radius^2
radius=1.25

diameter=2radius
radius=1.25
diameter=2(1.25)=2.5
3 balls so 2.5 times 3=7.5=height

aprox pi to 3.14
volume=7.5 times 3.14 times 1.25^2=7.5 times 3.14 times 1.5625=36.7969
a=36.7969


b. volume of balls
volume of sphere=4/3 times pi times radius^3
radius=1.25
v=4/3 times 3.14 times 1.25^3=4/3 times 3.14 times 1.95313=8.17708
then times 3 because 3 balls
8.17708 times 3=24.5312
b=24.5312



a=36.7969
b=24.5312
a-b=36.7969-24.5312=12.2656
normally rounded to the nearest 10th so
space=12.3 cubic inches or 12.3 in^3


volume of space=12.3 in^3







ANSWER

1. the volume sise is times8
2. 12.3 in^3




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