A room in the form of a cylinder surmounted by a hemishperical vaulted dome contains 17.7m^(3) of air, and the internal diameter of the building is equal to the height of the dome above the floor. Find the height of the building.

A rent is in the shape of a cylinder surmounted by a conical top. If the height and diameter of the cylindrical part are 2.1 m and 4m respectively , and the slant height of the top is 2.8m, find the area of the canvas used for making the tent. Also. find the cost of the canvas of the tent at the rate of Rs 500 "per"m^(2) ( Note that the base of the tent will not be covered with canvas. )

A toy is in the form of a hemisphere surmounted by a right circular cone of same base radius. If the radius of the base of the cone is 21 cm and its volume is 2/3 volume of hemisphere, calculate the height of the cone and the total curved surface area of the toy.

The diameter of the base of cylinder is 2 m and height is 1.8 m is method to recast a cone of diameter 3 m, find the height of cone .

A solid toy is in the form of a hemisphere surmounted by a right circular cone. The height of the cone is 2 cm and the diameter of the base is 4 cm. find the volume of the toy. If a right circular cylinder circumscribes the toy, find the difference in volume of cylinder and the toy.

A flower vase is in the form of a frusturn of a cone. The perimeters of its bases are 44 cm and 8.4 pi cm, if the depth is 14cm, then find how much soil it can hold. OR A toy is in the form of a cone mounted on a hemisphere both are of same radius. The diameter of the conical portion is 6cm and its height is 4cm. Determine the surface area of the solid. (taken pi =3.14 )

A window in a building is at a height of 10 m from the ground. The angle of depression of a point P on the ground from the window is 30^(@) . The angle of elevation of the top of the building from the point P is 60^(@) . Find the height of the building.

A tent consists of a frustum of a cone surmounted by a cone. If the diameter of the lower and upper circular ends of the frustum be 14 m and 26 m respectively, the height of the frustum be 8 m, and the slant height of the surmounted conical portion be 12m, find the area of canvas required to make the tent assuming the radii of the upper circular end and the base of surmounted conical portion are equal.

A solid wooden toy is in the form of a hemisphere surmounted by a cone of same radius. The radius of hemisphere is 3.5 cm and the total wood used in making of toy is 166(5)/(6)cm^(3) . Find the height of the toy. Also find the cost of painting the hemispherical part of the toy at the rate of Rs. 10 per cm^(2) (take pi=(22)/(7) )

A done of a building is in the form of a hemishphere. From inside, it was white- washed at the cost of Rs 498.96. If the cost of white - washing is Rs 2.00 per square metre, find the volume of the air inside the dome.