The short and the long hands of a wall clock are $8$ cm and $12$ cm respectively. Find the sum of the distance traveled by their tips in $3$ days. Give your answer in terms of $\pi$.
My solution:
Short hand:
Distance traveled in $12$ hours $= 2πr = 16π$ cm
$\Rightarrow$ Distance traveled in $3$ days$ = 3 \times 2 \times 16π = 96π$ cm
Long hand:
Distance traveled in $12$ hours $= 2πr = 24π$ cm
$\Rightarrow$ Distance traveled in $3$ days $= 3 \times 2 \times 24π = 144π$ cm
Sum of distances = $240π$ cm
But the correct answer is $1824π$ cm. How?