CAT (QA) PYQs

A ball of diameter $4$ cm is kept on top of a hollow cylinder standing vertically. The height of the cylinder is $3$ cm, while its volume is $9 \pi$ cm$^3$. Then the vertical distance, in cm, of the topmost point of the ball from the base of the cylinder is

A solid right circular cone of height $27$ cm is cut into pieces along a plane parallel to its base at a height of $18$ cm from the base. If the difference in volume of the two pieces is $225$ cc, the volume, in cc, of the original cone is

A solid metallic cube is melted to form five solid cubes whose volumes are in the ratio $1: 1 : 8: 27: 27$. The percentage by which the sum of the surface areas of these five cubes exceeds the surface area of the original cube is nearest to :