CUET UG 2024 — Geometry

In triangle $ABC$, points $D$ and $E$ are on $AB$ and $AC$ respectively such that $DE$ is parallel to $BC$. If $AD = 6$ cm, $DB = 4$ cm, $AE = 9$ cm, then the length of $EC$ (in cm) is:

In a square, lengths of the diagonals are $(4k + 6)$ cm and $(7k − 3)$ cm. The area of the square (in cm²) is:

The volume of a cylinder having base radius 3 cm is 396 cm³. Find its curved surface area (in cm²):