Surface Areas a...

A cone of radius $$r$$ and height '$$3h$$' is cut by two planes parallel to the base at height $$h$$ and $$20 h$$. The volumes of three parts of the cone are in the ratio :

If a cubical metal of dimensions 44 cm $$\times$$ 30 cm $$\times$$ 15 cm was melted and cast into a cylinder of height of 28 cm, then what is its radius?

A spherical glass vessel has a cylindrical neck 8 cm long, 2 cm in diameter; the diameter of the spherical part is 8.5 cm. By measuring the amount of water it holds, a child finds its volume to be 345 $$cm^{3}$$. Check whether she is correct, taking the above as the inside measurements, and $$\pi$$ = 3.14

A toy is in the form of a cone of radius $$3.5$$ cm mounted on a hemisphere of same radius. The total height of the is $$15.5$$ cm. Find the total surface area of the toy.

A tent 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 4 m respectively, and the slant height of the top is 2.8 m, 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 solid is in the shape of a cone standing on a hemisphere with both their radii being equal to 1 cm and the height of the cone is equal to its radius. Find the volume of the solid in terms of $$\pi$$.

A vessel is in the form of a hollow hemisphere mounted by a hollow cylinder. The diameter of the hemisphere is 14 cm and the total height of the vessel is 13 cm. Find the inner surface area of the vessel.

A drinking glass in the shape of a frustrum of a cone of height $$14$$ cm.Two diameters of its two circular ends are $$4$$ cm. and $$2$$ cm, then the capacity of glass is:

The dimensions of a solid metal cuboid are $$72\, cm\, \times\, 30\, cm\, \times\, 75\, cm.$$ it is metaled and recast into identical solid metal cubes with edge of each $$6$$ cm. Find the number of cubes formed.
Also, find the cost of polishing the surface of all the cubes formed at the rate Rs. $$150$$ per sq. m.

A medicine capsule is in the shape of a cylinder with two hemisphere struck to each of its ends (see figure). The length of the entire capsule is $$14 mm$$ and the diameter of the capsule is $$5 mm$$. Find its surface area.