The greenhouse pictured below can be modeled as a rectangular prism with a half-cylinder on top. The rectangular prism is 20 feet wide, 12 feet high, and 45 feet long. The half-cylinder has a diameter of 20 feet.
To the nearest cubic foot, what is the volume of the greenhouse?
Since the greenhouse comprises of a rectangular prism and half a cylinder, the volume of the railing = volume of rectangular prism + half the volume of a cylinder.
Volume of rectangular prism = L x H x W.
Where H is the height of the rectangular section of the greenhouse, H is the height of the rectangular section of the greenhouse and W is the width of the rectangular section of the greenhouse.
Thus, volume of the rectangular section of the greenhouse = 45 x 20 x 12
Volume of cylinder = πr2h. Where r is the radius and h is the height.
radius = diameter/2 = 20/2 = 10
volume of the cylindrical section = π x (10)2 x 45
Thus, half the volume = 4500π/2
Therefore, the total volume = 10800 + 2250π