Surface Areas a...

A solid cone of radius $$r$$ and height $$h$$ is placed over a solid cylinder having same base radius and height as that of a cone. The total surface area of the combined solid is 

A medicine-capsule is in the shape of a cylinder of diameter $$0.5$$cm with two hemispheres stuck to each of its ends. The length of entire capsule is $$2$$cm. The capacity of the capsule is

A cone is $$8.4\ cm$$ high and the radius of its base is $$2.1\ cm$$. It is melted and recast into a sphere. The radius of the sphere is

A metallic spherical shell of internal and external diameters $$4 $$ cm and $$8 $$ cm, respectively is melted and recast into the form a cone of base diameter $$8 $$ cm. The height of the cone is

The diameters of the two circular ends of the bucket are $$44 $$ cm and $$24 $$ cm. The height of the bucket is $$35$$ cm. The capacity of the bucket is

The diameter of a metallic sphere is $$6 cm$$. It is melted and drawn into a wire of diameter $$2 cm$$, then the length of the wire is

A frustum of a right circular cone of height $$16\text{ cm}$$ with radii of its circular ends as $$8\text{ cm}$$ and $$20\text{ cm}$$ has its slant height equal to:

The side of a square is $$2$$ cm and  semicircles are constructed  on each side of the square, then  the area of the whole figure is

A building is in the form of a cylinder surmounted by a hemispherical vaulted dome and contains $$41\dfrac{19}{21}\ m^3$$ of air. If the internal diameter of dome is equal to its total height above the floor, find the height of the building.

Two solid cones $$A$$ and $$B$$ are placed in a cylindrical tube as shown in the figure. The ratio of their capacities is $$2:1$$. Find their heights.