A cylindrical hole of diameter `30cm` is bored through a cuboidal wooden block with side `1 meter` Find the volume of the object so formed (`pi=3.14`)

The largest possible sphere is carved out of a wooden solid cube of side 7cm. Find the volume of the wood left. (Use pi=(22)/7)dot

If a wooden right circular cylinder with radius 2 meters and height 6 meters has a cylindrical hole of diameter 2 meters drilled through the center as shown, what is the entire surface area (including the top and bottom faces), in square meters, of the resulting figure ?

Find the area of a circle of radius 30 cm (use pi=3.14 )

Six cubes each of side 12 cm are joined end to end .Find the surface area of the cuboid so formed .

A right triangle ABC with its sides 5 cm, 12cm and 13cm is revolved about the side 12cm. Find the volume of the solid so formed. If the triangle ABC is revolved about side 5cm, then find the volume of the solid so obtained. Find also the ratio of the volumes of the two solids obtained.

A right triangle ABC with its sides 5 cm, 12cm and 13cm is revolved about the side 12cm. Find the volume of the solid so formed. If the triangle ABC is revolved about side 5cm, then find the volume of the solid so obtained. Find also the ratio of the volumes of the two solids obtained.

A toy is in the form of a cone mounted on a hemisphere with the same radius. The diameter of the base of the conical portion is 12 cm and its height is 8 cm. Determine the surface area and the volume of the toy (pi = 3.14).

A cylindrical vessel with internal diameter 10 cm and height 10.5 cm is full of water. A solid cone of base diameter 7 cm and height 6 cm is completely immersed in water. Find the volume of water (i) displaced out of the cylinder (ii) left in the cylinder. (Take pi=22//7 )

A cylindrical tank has a hole of diameter 2r in its bottom. The hole is covered wooden cylindrical block of diameter 4r, height h and density rho//3 . Situation I: Initially, the tank is filled with water of density rho to a height such that the height of water above the top of the block is h_1 (measured from the top of the block). Situation II: The water is removed from the tank to a height h_2 (measured from the bottom of the block), as shown in the figure. The height h_2 is smaller than h (height of the block) and thus the block is exposed to the atmosphere. Find the minimum value of height h_1 (in situation 1), for which the block just starts to move up?

A cylindrical tank has a hole of diameter 2r in its bottom. The hole is covered wooden cylindrical block of diameter 4r, height h and density rho//3 . Situation I: Initially, the tank is filled with water of density rho to a height such that the height of water above the top of the block is h_1 (measured from the top of the block). Situation II: The water is removed from the tank to a height h_2 (measured from the bottom of the block), as shown in the figure. The height h_2 is smaller than h (height of the block) and thus the block is exposed to the atmosphere. Find the minimum value of height h_1 (in situation 1), for which the block just starts to move up?