An object is made of a prism with a spherical cap on its square shaped top. The cap's base has a diameter equal to the lengths of the top. The prism's height is # 7 #, the cap's height is #4 #, and the cap's radius is #8 #. What is the object's volume?

1 Answer
Jan 18, 2018

Answer:

It's a trickily-written question: we need to deduce that it's a sphere on a square prism. It is also not clear whether the top is spherical or hemispherical. The volume of the object is #716# or #582# cubic units (we are not told what units are used).

Explanation:

Volume of the sphere: #V=4/3pir^3=4/3xx3.14159xx8^2=268# cubic units

If the cap is a hemisphere, its volume will be half this, #134# cubic units

The square has side length #8# units (we also need to deduce this from the question).

Volume of square prism: #V=lxxbxxh=8xx8xx7=448# cubic units.

If the cap is a full sphere, the total volume is #268+448=716# cubic units.

If the cap is a hemisphere, the total volume is #134+448=582# cubic units.

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