Answer:
Explanation:
You want a formula for the volume of the given figure, which is a hemisphere of radius r atop a cylinder of the same radius and height r.
Volume formulas
The volume of a sphere is given by ...
V = (4/3)πr³
The volume of a cylinder is given by ...
V = πr²h
Composition
The given figure is composed of half a sphere, and a cylinder. The total volume will be the sum of the volumes of these parts.
total volume = 1/2(sphere volume) + (cylinder volume)
A Total volume
Using a height of r for the cylinder, we can substitute the above formulas to get ...
total volume = 1/2(4/3πr³) +(πr²·r)
total volume = 2/3πr³ + πr³ = (2/3 +1)πr³
total volume = (5/3)πr³
B How much glass
When the height is 12 inches, the radius is 6 inches, so the volume of the object is ...
total volume ≈ (5/3)(3.14)(6 in)³ = 1130.4 in³
About 1130.4 cubic inches of glass will be needed for a paperweight that is 12 inches tall.