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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 `pi`

Respuesta :

katyyym35
Given:
Cylinder: height = 16 cm ; radius = 5 cm
cone: height = 12 cm ; radius = 4 cm

Volume of cylinder = 3.14 * (5cm)² * 16cm = 1,256 cm³
Volume of cone = 3.14 * (4cm)² * 12cm/3 = 200.96 cm³

Volume of air space = 1256 cm³ - 200.96 cm³ = 1,055.04 cm³ 

Answer:

1055.04 cm³

Step-by-step explanation:

Since, when the cone is placed inside the cylinder,

Then, the volume of the air space surrounding the cone inside the cylinder = Volume of the cylinder - Volume of the cone.

Since, the volume of a cylinder is,

[tex]V=\pi r^2h[/tex]

Where, r is the radius and h is the height,

Here, h = 16 cm, r = 5 cm,

So, the volume of the cylinder is,

[tex]V_1=\pi (5)^2 (16)[/tex]

[tex]=3.14\times 25\times 16[/tex]

[tex]=1256\text{ cubic cm}[/tex]

Now, the volume of a cone is,

[tex]V=\frac{1}{3}\pi (R)^2 H[/tex]

Where, R is the radius and H is the height,

Here, R = 4 cm and H = 12 cm,

So, the volume of the cone is,

[tex]V_2=\frac{1}{3}\pi (4)^2 (12)[/tex]

[tex]=\frac{1}{3}\times 3.14\times 16\times 12[/tex]

[tex]=200.96\text{ cubic cm}[/tex]

Hence, the volume of the air space surrounding the cone inside the cylinder is,

[tex]V_1-V_2=1256-200.96=1055.04\text{ cubic cm}[/tex]

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