A conical vessel whose internal base radius is 18 cm and height 60 cm is full of a liquid. The entire liquid of the vessel is emptied into a cylindrical vessel with internal radius 15 cm. The height (in cm) to which the liquid rises in the cylindrical vessel is:

The areas of the three adjacent faces of a cuboid are 32 cm², 24 cm² and 48cm². What is the volume of the cuboid?

The diameter of a roller is 84 cm and its length is 120 cm. It makes 500 complete revolutions to move once over to level a playground. Find the area of the playground.

A right circular cone of largest volume is cut out from a solid wooden hemisphere. The remaining material is what percentage of the volume of the original hemisphere?

If the ratio of the areas of two similar triangle ABC and DEF is 36:81 and EF = 6.9 cm., then BC is equal to –

A straight line parallel to the base QR of the ∆PQR intersect PQ and PR at the points S and T respectively. If the area of the ∆PQT be 36 cm² then area of the ∆PRS is:

Three solid metallic sphere whose radii are 3cm, x cm and 18cm respectively, are melted and recast into a single solid sphere of diameter 38cm. Then find the total surface area of the sphere with radius x cm?

The diagonal of a square is equal to the side of an equilateral triangle. If the area of the square is $$ {18\sqrt{3}}$$ sq.cm. What is the area (in cm²) of the equilateral triangle ?