Length of diagonal of a cube is 3 √3 cm. Find the volume of the cube.

The length of the diagonal of each face of a cube is 6√2 cm. Find the total surface area of the cube.

The length of the diagonal of a cube is 4√3 cm. Calculate the total surface area of the cube.

The sum of length, breadth and height of a cuboid is 10 cm and the length of the diagonal is √32 cm. Find the area of the surfaces of the cuboid.

Half of a cuboidal water tank with length of 2.1 m and breadth of 1.5 m is filled with water. If 630 liters of water is poured into the tank, then calculate the increased height of water.

If the length, breadth, and height of a rectangular parallelopiped are equal, then the special name of this solid is ___.

If 75 buckets of water of equal measure are taken out from the water of a cubical water-filled-tank, then th of the water remains in the tank. If the length of one edge of the tank is 1.5 metres, then calculate the quantity of water in litre that can be held in each bucket.

The inner length, breadth, and height of a tea box are 7.5 dm, 6 dm, and 5.4 dm respectively. If the weight of the box filled with tea is 52 kg 350 gm, but in the empty state, its weight is 3.75 kg, then calculate the weight of 1 cubic dm of tea.

Find the mean proportion of xy² and xz²

The ratio of portion of profit of two friends is 1/2 : 1/3. Find the ratio of their capitals

If sin (θ + 30°) = cos 15°, then find the value of cos 2θ.

From an external point P of a circle with centre O, two tangents PS and PT are drawn. QS is a chord of the circle parallel to PT. If ∠SPT = 80°, then find the value of ∠QST.