Volumes
In order to compare both volumes we want to find the volume of each figure:
Volume of the cylinder
In order to find its volume we first find the area of its base.
Since its base is a circle, its area is given by
base area = π · r²,
where π and r are numbers:
π is pi and r is the radius of the base.
Since
π = 3.14
and
r = 2 in,
then
base area = 3.14 · (2 in)²
= 3.14 · 4 in²
= 12.56 in²
The volume is the product of the base area by the height of the cylinder:
volume cylinder = base area · height
volume cylinder = π · r² · h
= 12.56 in² · 8 in
= 100.48 in³
Then, the volume of the cylinder is 100.48 in³.
Volume of the cone
As we did before, in order to find its volume we first find the area of its base.
We use the equation
base area = π · r²,
where
π = 3.14
and
r = 3 in.
Then
base area = 3.14 · (3 in)²
base area = 28.26 in²
We multiply the base area by 1/3 the height (10 in) of the cone
cone volume = 1/3 · base area · height
cone volume = 1/3 · π · r² · h
= 1/3 · 28.26 in² · 10 in
= 94.2 in³
Then, the volume of the cone is 94.2 in³.
Comparison
Since the volume of the cylinder is 100.48 in³ and the volume of the cone is 94.2 in³. We observe that the volume of the cylinder is bigger (it takes up more space than the cone).
Since
100.48 in³ - 94.20 in³ = 6.28 in³
Then the volume of the cylinder is 6.28 in³ greater than the cone's volume.
Answer: B