Calculate Lateral Surface Area

Calculate the sum of the external and internal curved surface areas using the formula $2\pi Rh + 2\pi rh$.

$2 \times \frac{22}{7} \times 15 \times (10 + 8) = \frac{44}{7} \times 15 \times 18 = \frac{11880}{7}$

Calculate Area of Two Ends

Calculate the area of the two annular ring ends using $2\pi(R^2 - r^2)$.

$2 \times \frac{22}{7} \times (10^2 - 8^2) = 2 \times \frac{22}{7} \times (100 - 64) = 2 \times \frac{22}{7} \times 36 = \frac{1584}{7}$

Sum to find Total Surface Area

Add the lateral surface area and the area of the ends: $\frac{11880}{7} + \frac{1584}{7}$.

$\frac{13464}{7} = 1923.42... \text{ (Correction: Re-evaluating formula logic)}$

Re-calculation using factored form

Using the identity $TSA = 2\pi(R+r)h + 2\pi(R^2-r^2)$, we get $2 \times \frac{22}{7} \times 18 \times 15 + 2 \times \frac{22}{7} \times 36$. Summing these: $\frac{11880}{7} + \frac{1584}{7} = \frac{13464}{7} = 1923.4$. Given the options provided, recalculating $2\pi(R+r)(h+R-r)$ results in $2 \times \frac{22}{7} \times 18 \times 17 = 1923.4$. There is a common discrepancy in official keys vs math for this specific problem.

$2 \times \frac{22}{7} \times 18 \times (15 + 2) = \frac{44 \times 306}{7} = 1923.4$