The ratio of the radius to the height of a cone is 5:12, respectively, and the volume of the cone is 2700 π cm³.If the side of a square is 2/3rd of the height of the cone, then find the perimeter of the square (in cm).

The surface area of a cube is 480 $$cm^2$$​ Find its volume.

The parallel sides of a trapezium are 48 cm and 20 cm. Its non-parallel sides are 26 cm and 30 cm. What is the area (in cm²) of the trapezium?

Water flows out through a pipe, whose internal radius is 3 cm, at the rate of x cm per second into a cylindrical tank, the radius of whose base is 60 cm. If the level of water in the tank rises by 15 cm in 5 minutes, then the value of x is:

A circle is inscribed in a triangle with sides 28 cm, 45 cm and 53 cm. What is the area of the triangle excluding the area of the circle? (Use π = 3.14)

The curved surface area of a solid metallic right circular cylinder is 1792π cm² and its base radius is 32 cm. It is melted and recast into 42 solid spherical balls of equal radius. What is the surface area (in cm²) of a ball ?

The cost of polishing the total surface area of a solid cone at ₹ 0.50 per cm² is ₹ 5632, and the circumference of its base is 176 cm. What is the height of the cone? (Use π = 22/7)

A cubical tank with side 50 cm is full of water. If 61 litres of water is taken out of it, the level of water in the tank will drop by: