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
