Question

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?

Answer 1

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.