Question

30 POINTS PLSSS HELP

Part 1: Design three ice creams cones with different dimensions for radius and height. The three cones can be classified as scaled similar figures. Record the measurements for your design in the table below.


Part II: Volume

Determine the effect that scaling has on the volume of the cones. Calculate the volume for each of the cones. Show all of your work in the space provided.


a. Volume of Cone 1:






b. Volume of Cone 2:






c. Volume of Cone 3:






d. What effect does the scaling have on the volume?





Part III: Cost

Suppose one ounce of ice cream costs that consumer $0.50. How does scaling relate to the cost of the cone?

Answer 1

Part 1) 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) 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*r²*h
where
r is the radius
h is the height

a) Find Volume of Cone 1:
r=4 cm
h=6 cm
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 2
scale 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 3
scale 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) 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 1
volume cone 1=100.53 cm³
convert to ounces
1 cm³ is equal to 0.033814 ounces
100.53 cm³*0.033814=3.40 ounces
3.40 ounces*$0.50----> $1.70


find the cost of the cone 2
volume 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 3
volume 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

cost cone 2/cost cone 1=5.74/1.70----> 3.37
this is the scale factor raised to the cube

cost cone 3/cost cone 1=13.60/1.70----> 8
this is the scale factor raised to the cube

therefore

the answer is

the cost of the cone will increase by an amount equal to the scale factor raised to the cube