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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?

Mathematics 09/01/2020 01:00 AM answersmine

Answered @ 09/01/2020 01:00 AM By answersmine

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

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