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,
![V=\pi r^2h](https://tex.z-dn.net/?f=V%3D%5Cpi%20r%5E2h)
Where, r is the radius and h is the height,
Here, h = 16 cm, r = 5 cm,
So, the volume of the cylinder is,
![V_1=\pi (5)^2 (16)](https://tex.z-dn.net/?f=V_1%3D%5Cpi%20%285%29%5E2%20%2816%29)
![=3.14\times 25\times 16](https://tex.z-dn.net/?f=%3D3.14%5Ctimes%2025%5Ctimes%2016)
![=1256\text{ cubic cm}](https://tex.z-dn.net/?f=%3D1256%5Ctext%7B%20cubic%20cm%7D)
Now, the volume of a cone is,
![V=\frac{1}{3}\pi (R)^2 H](https://tex.z-dn.net/?f=V%3D%5Cfrac%7B1%7D%7B3%7D%5Cpi%20%28R%29%5E2%20H)
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,
![V_2=\frac{1}{3}\pi (4)^2 (12)](https://tex.z-dn.net/?f=V_2%3D%5Cfrac%7B1%7D%7B3%7D%5Cpi%20%284%29%5E2%20%2812%29)
![=\frac{1}{3}\times 3.14\times 16\times 12](https://tex.z-dn.net/?f=%3D%5Cfrac%7B1%7D%7B3%7D%5Ctimes%203.14%5Ctimes%2016%5Ctimes%2012)
![=200.96\text{ cubic cm}](https://tex.z-dn.net/?f=%3D200.96%5Ctext%7B%20cubic%20cm%7D)
Hence, the volume of the air space surrounding the cone inside the cylinder is,
![V_1-V_2=1256-200.96=1055.04\text{ cubic cm}](https://tex.z-dn.net/?f=V_1-V_2%3D1256-200.96%3D1055.04%5Ctext%7B%20cubic%20cm%7D)