Given:
Kiosk is the combination of a cylinder and a cone.
Diameter of cylinder and cone = 5 m
Height of the cylinder = 3 m
Height of the cone = 2 m
To find:
The volume of the kiosk.
Solution:
We know that the radius is half of the diameter. So,
Radius of cylinder and cone =
m
=
m
Volume of the cylinder is:
![V_1=\pi r^2h](https://tex.z-dn.net/?f=V_1%3D%5Cpi%20r%5E2h)
Where, r is the radius and h is the height of the cylinder.
Putting
in the above formula, we get
![V_1=(3.14)(2.5)^2(3)](https://tex.z-dn.net/?f=V_1%3D%283.14%29%282.5%29%5E2%283%29)
![V_1=(3.14)(6.25)(3)](https://tex.z-dn.net/?f=V_1%3D%283.14%29%286.25%29%283%29)
![V_1=58.875](https://tex.z-dn.net/?f=V_1%3D58.875)
Volume of a cone is:
![V_2=\dfrac{1}{3}\pi r^2h](https://tex.z-dn.net/?f=V_2%3D%5Cdfrac%7B1%7D%7B3%7D%5Cpi%20r%5E2h)
Where, r is the radius and h is the height of the cone.
Putting
in the above formula, we get
![V_2=\dfrac{1}{3}(3.14)(2.5)^2(2)](https://tex.z-dn.net/?f=V_2%3D%5Cdfrac%7B1%7D%7B3%7D%283.14%29%282.5%29%5E2%282%29)
![V_2=\dfrac{1}{3}(3.14)(6.25)(2)](https://tex.z-dn.net/?f=V_2%3D%5Cdfrac%7B1%7D%7B3%7D%283.14%29%286.25%29%282%29)
![V_2\approx 13.083](https://tex.z-dn.net/?f=V_2%5Capprox%2013.083)
The volume of the kiosk is the sum of volume of cylinder and the volume of cone.
![V=V_1+V_2](https://tex.z-dn.net/?f=V%3DV_1%2BV_2)
![V=58.875+13.083](https://tex.z-dn.net/?f=V%3D58.875%2B13.083)
![V=71.958](https://tex.z-dn.net/?f=V%3D71.958)
![V\approx 72](https://tex.z-dn.net/?f=V%5Capprox%2072)
Therefore, the volume of the kiosk is 72 cubic meter.