Part 1) <span>Design three ice creams cones with different dimensions for radius and height. The three cones can be classified as scaled similar figures.
the table in the attached figure
Part 2) </span><span>Determine the effect that scaling has on the volume of the cones. Calculate the volume for each of the cones
we know that
volume of a cone=(1/3)*pi*r</span>²*h
where
r is the radius
h is the height
a) Find <span>Volume of Cone 1:
r=4 cm
h=6 cm
</span>volume of a cone 1=(1/3)*pi*4²*6-----> 32*pi cm³----> 100.53 cm³
b) Find Volume of Cone 2:
r=6 cm
h=9 cm
volume of a cone 2=(1/3)*pi*6²*9-----> 108*pi cm³----> 339.29 cm³
c) Find Volume of Cone 3:
r=8 cm
h=12 cm
volume of a cone 1=(1/3)*pi*8²*12-----> 256*pi cm³----> 804.25 cm³
compare cone 1 and cone 2scale factor=measure radius cone 2/measure radius cone 1
scale factor=6/4----> 1.5
volume cone 2/volume cone 1=(108*pi)/(32*pi)----> 3.375
3.375=1.5³
so
3.375=scale factor³
therefore
volume of cone 2=[scale factor]³*volume of cone 1
compare cone 1 and cone 3scale factor=measure radius cone 3/measure radius cone 1
scale factor=8/4----> 2
volume cone 3/volume cone 1=(256*pi)/(32*pi)---->8
8=2³
so
8=scale factor³
therefore
volume of cone 3=[scale factor]³*volume of cone 1
the answer part d)
the scaling increase the volume by an amount equal to the scale factor raised to the cube
Part 3) <span>Suppose one ounce of ice cream costs that consumer $0.50. How does scaling relate to the cost of the cone?
find the cost of the cone 1volume cone 1=100.53 cm</span>³
<span>convert to ounces
1 cm</span>³ is equal to 0.033814 ounces
100.53 cm³*0.033814=3.40 ounces
<span>3.40 ounces*$0.50----> $1.70
</span>
find the cost of the cone 2volume cone 1=339.29 cm³
convert to ounces
1 cm³ is equal to 0.033814 ounces
339.29 cm³*0.033814=11.47 ounces
11.47 ounces*$0.50----> $5.74
find the cost of the cone 3volume cone 1=804.25 cm³
convert to ounces
1 cm³ is equal to 0.033814 ounces
804.25 cm³*0.033814=27.19 ounces
27.19 ounces*$0.50----> $13.60
<span>
cost cone 2/cost cone 1=5.74/1.70----> 3.37
this is the scale factor raised to the cube
</span>cost cone 3/cost cone 1=13.60/1.70----> 8
this is the scale factor raised to the cube<span>
therefore
the answer is
</span>
the cost of the cone will increase by an amount equal to the scale factor raised to the cube <span>
</span>