Volume of a Composite Geometric Shape
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A sand castle built in the shape of a cylinder and a right cone is constructed. The internal measurements of the sand castle are represented in the figure above. Of the following, which is closest to the volume of the sand castle, in cubic feet? (A) $120,000\pi$
This question includes visual content: A composite 3D object consisting of a cylinder at the bottom and a cone on top. The cylinder has a height of 200 ft and a radius of 20 ft. The cone sits on top of the cylinder, sharing the same 20 ft radius base, and has a height of 300 ft.
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Let's find the total volume of this sand castle, which consists of a cylinder topped by a right cone.
Volume of a Composite Solid
First, let's identify the dimensions from the diagram. Both the cylinder and the cone share the same radius.
The height of the cylindrical base is two hundred feet.
And the height of the conical top is three hundred feet.
The total volume is the sum of the volume of the cylinder and the volume of the cone.
Step 1: Volume of the Cylinder
Substitute the radius of twenty and height of two hundred into the cylinder formula.
Since twenty squared is four hundred, we multiply four hundred by two hundred to get eighty thousand.
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