A food court is investigating which paper cups to use for its water fountain. Which best compares the volumes of cup A and cup B?

D. The volume of A is half the volume of B

Step-by-step explanation:

Looking at the diagram of the paper cups used for its fountain, it is shaped as a cone.

Therefore, the volume of a cone =

1/3πr²h

Where r = radius and h = height

For Paper cup(cone) A

r = r

h = 2r

Volume of the cone = 1/3πr²h

= 1/3 × π × r² × 2r

= 1/3 × π × r² × 2(r)

= 1/3 × π × r² × 2 × r

= 2/3( πr³)

For Paper cup(cone) B

r = 2r

h = r

Volume of the cone = 1/3πr²h

= 1/3 × π × (2r)² × r

= 1/3 × π × 4r² × r

= 1/3 × π × 4r³

= 4/3( πr³)

Comparing the Volume of A to the Volume of B

2/3( πr³) : 4/3( πr³)

2/3( πr³) : 2[2/3( πr³)]

From the above ratio and comparison, we can see that The Volume of Cone B is twice the Volume of Cone A.

Therefore, this means The volume of A is half the volume of B

d

step-by-step explanation: