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
David G.
Jan 18, 2018

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=43πr3=43×3.14159×82=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=l×b×h=8×8×7=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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