A sculptor is planning to order a cylinder of composite stone to sculpt a full-sized person. The figure will be 6 feet tall, and 2' at the longest diameter. The composite stone weighs 50 pounds per cubic foot. About how much will the smallest cylinder weigh that the sculptor can order to make his statue?

The answer is 942 pounds.

The volume (V) of the cylinder is:

V = π r² h,

where:

r - the radius of the cylinder,

h - the height of the cylinder.

It is given:

diameter d = 2r = 2 feet ⇒ r = 1 foot

h = 6 feet

Thus,

V = π r² h = 3.14 · (1 foot) ² · 6 feet = 18.84 cubic feet

Now, using the proportion, we will calculate how many composite stone it should be ordered:

50 pounds : 1 cubic foot = x : 18.84 cubic feet

After crossing the products:

x = 50 pounds · 18.84 = 942 pounds.

R=D/2=2/2=1

V (cylinder) = π*R²*H = π*1²*6=6π feet³

Weigh = 6π*50=300*π≈942 pounds