You are given a $10 roll of quarters. Knowing each quarter has a diameter of 0.955 inches and is 0.065 inches thick, what is the volume of the quarters in liter

Question

You are given a $10 roll of quarters. Knowing each quarter has a diameter of 0.955 inches and is 0.065 inches thick, what is the volume of the quarters in literA? (hint: assume each quarter is a cylinder.)

Answer 1

How many quarters are in a 10$ roll? Four quarters make a dollar, so 4×10 = 40 quarters.

 

The roll of quarters is a cylinder. The volume of a cylinder is the area of the top (circular part) multiplied by the length or height (depending on how you look at it).

 

If each of the 40 quarters are 0.065 inches thick then the height of the roll of quarters is: 40×0.065 = 2.6 inches

 

So now we just need to multiply this, height by the area of the top. The diameter which is twice the radius is given to be: 0.955 inches. That means the radius; 0.955 ÷ 2 = 0.4775 inches

 

Area of a circle = πr²

Volume of a cylinder = πr²h

 

Volume of the roll = π(0.4775)²(2.6)

Volume of the roll = π(0.593)

Volume of the roll = 1.86 in³