A cylinder has a height of 16cm and a radius of 5cm. A cone has a height of 12cm and a radius of 4cm. What is the volume of the air space surrounding the cone Inside the cylinder?

Cylinder:

Height: h1=16 cm

Radius: r1=5 cm

Volume: V1=?

V1=pi (r1) ^2 h1

V1 = pi (5 cm) ^2 (16 cm)

V1 = pi (25 cm^2) (16 cm)

V1=400 pi cm^3

Cone:

Height: h2=12 cm

Radius: r2=4 cm

Volume: V2=?

V2=pi (r2) ^2 h2 / 3

V2 = pi (4 cm) ^2 (12 cm) / 3

V2 = pi (16 cm^2) (12 cm) / 3

V2=64 pi cm^3

Volume of the air space surrounding the cone inside the cylinder: V=?

V=V1-V2

V=400 pi cm^3 - 64 pi cm^3

V=336 pi cm^3

V=336 (3.1416) cm^3

V = 1,055.5776 cm^3

V=1,055.58 cm^3

Answer: The volume of the air space surrounding the cone inside the cylinder is 336 pi cm^3 = 1,055.58 cm^3