# 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?

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: $V = \frac{4}{3} \pi {r}^{3} = \frac{4}{3} \times 3.14159 \times {8}^{2} = 268$ 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: $V = l \times b \times h = 8 \times 8 \times 7 = 448$ 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.