Answer:
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
