Find the surface area of each of the two labeled ganzas in terms of ππ, rounded to the nearest thousandths and as a decimal, round to the nearest whole number. The weight of the smaller ganza is 1.1 pounds. Assume that the surface area is proportional to the weight. What is the weight of the larger ganza to the nearest tenth of a pound? The smaller ganza is the radius is 3.5 and the length is 10. The larger ganza is the radius is 5.5 and the length is 24.5

The surface area of the smaller ganza is 94.5π, the surface area of the larger ganza is 330π, and the weight of the larger ganza is 3.8 lbs.

The surface area of a cylinder is found by using the formula

SA=2πr²+πdh. This is based on the formula for the area of a circle, with there being two circles on the cylinder; and the circumference of a circle, which is the length of the rectangle "wrapped around" the cylinder, multiplied by the length of the cylinder.

Substituting our known information for the small ganza we have:

SA=2π (3.5²) + π (7) (10) [if the radius is 3.5, the diameter is 2*3.5=7]

Simplifying, we have:

SA=24.5π+70π=94.5π

Substituting the known information for the large ganza we have:

SA=2π (5.5²) + π (11) (24.5)

Simplifying, we have:

SA=60.5π+269.5π=330π

We set up a proportion to find the weight of the large ganza:

94.5π/1.1 = 330π/x

Cross multiplying we have:

94.5π*x = 330π*1.1

94.5πx=363π

Divide both sides by 94.5π:

94.5πx/94.5π = 363π/94.5π

x ≈ 3.8