Four pieces of cake cost $10. How much do eleven pieces of cake cost?

Given that four pieces of cake cost 10, we can find the cost per piece by dividing the total cost by the number of pieces. $$ \text{Cost per piece} = \frac{\10}{4 \text{ pieces}} $$ \text{Cost per piece} = $2.50 \text{ per piece} $$

Now that we know the cost of one piece, we multiply this by 11 to find the cost of eleven pieces. $\text{Cost of 11 pieces} = \$2.50/\text{piece} \times 11 \text{ pieces}$ $\text{Cost of 11 pieces} = \$27.50$

The cost of eleven pieces of cake is $27.50.

\boxed{\27.50}$