Question

Chase has two stacks of coins, one stack is made up of 12 quarters and the other stack is made up of 12 pennies. He says that the total area of the two shapes is equal. Is he correct?

Answer 1

The total area of the two shapes is not equal, Chase is wrong

Explanation:

we know that

The surface area of a cylinder is given by the formula

`SA=2\pi r^(2) +2\pi rh`

where

r is the radius of the coin

h is the thickness of the coin

we have

Penny

The coin is 19.05 mm in diameter and 1.52 mm in thickness.

so

`r=19.05/2=9.525\ mm`

`h=1.52(12)=18.24\ mm`

substitute in the formula

`SA=2\pi (9.525)^(2) +2\pi (9.525)(18.24)`

`SA=181.451\pi +347.472\pi`

`SA=528.92\pi\ mm^2`

Quarter

The diameter is 24.26 mm and 1.75 mm in thickness.

so

`r=24.26/2=12.13\ mm`

`h=1.75(12)=21\ mm`

substitute in the formula

`SA=2\pi (12.13)^(2) +2\pi (12.13)(21)`

`SA=294.27\pi +509.46\pi`

`SA=803.73\pi\ mm^2`

therefore

The total area of the two shapes is not equal, Chase is wrong, because the coins have different diameter and thickness