Question

1. toonies (canada’s two - dollar coins) are wrapped in plastic rolls that are worth $50.00. a toonie has a diameter of 1.0625 inches and a height of 0.125 inches.

a. how many toonies are in a $50.00 roll?
b. determine the height of the roll.
c. determine the surface area of the plastic roll that fits $50.00 worth of toonies. round to three decimal places.

Explanation:

Step1: Calculate number of toonies in a roll

Since each toonie is worth $2 and a roll is worth $50, we divide the total value of the roll by the value of one toonie.
$n=\frac{50}{2}=25$

Step2: Determine height of the roll

Each toonie has a height of 0.125 inches. The height of the roll is the height of one toonie times the number of toonies in the roll.
$h = 0.125\times25=3.125$ inches

Step3: Calculate surface - area of the plastic roll

The plastic roll is a cylinder. The diameter of the roll is the same as the diameter of a toonie, $d = 1.0625$ inches (so the radius $r=\frac{1.0625}{2}=0.53125$ inches), and the height of the roll $h = 3.125$ inches. The surface - area formula for a cylinder is $A = 2\pi r(r + h)$.
$A=2\pi\times0.53125\times(0.53125 + 3.125)$
$A=2\pi\times0.53125\times3.65625$
$A=\pi\times0.53125\times7.3125$
$A\approx12.257$ square inches

Answer:

a. 25
b. 3.125 inches
c. 12.257 square inches