Question

A cylinder has a height of 16 cm and a radius of 5 cm. A cone has a height of 12 cm and a radius of 4 cm. If the cone is placed inside the cylinder as shown, what is the volume of the air space surrounding the cone inside the cylinder? (Use 3.14 as an approximation of π.)

Answer 1

volume of cylinder(
`A_1`)
`=(1)/(3)h \pi r^2`
volume of cone(
`A_2`)
`=h \pi r^2`
plugging stuff in we get

`A_1= (1)/(3)*16*5^2= (400)/(3)`

`A_2= 12*4^2= 192`
Which the empty space
`=A_2-A_1=192- (400)/(3) = (176)/(3)`

Answer 2

Cylinder:
r = 5 cm, h = 16 cm
V = r² π h
V = 5² π · 16 = 25 · 3.14 · 16 = 1,256 cm³
----------------------------------------------------
Cone:
r = 4 cm, h = 12 cm
V = 1/3 r² π h
V = 1/3 · 4² π · 12 = 200.96 cm³
The volume of the air space :
1,256 - 200.96 = 1,055.04 cm³