Surface Areas a...

A solid is in the form of a right circular cone mounted on a solid hemisphere with the same radius is made from a piece of metal. The radius of the hemisphere is $$\displaystyle \frac{1}{3}$$ of the vertical height of the conical part. If the radius of the base of the cone is $$r$$, the volume of the piece of metal is

A vessel is in the form of a hemispherical bowl, surmounted by a hollow cylinder. The diameter of the hemisphere is $$12\ \text{cm}$$ and the total height of the vessel is $$16\ \text{cm}$$. Find the capacity of the vessel. (Take $$\pi$$ = 22/7). Also find the internal surface area of the vessel.

A solid toy is in the form of a right circular with hemispherical ends. The total height of the solid is 19 cm and diameter of the cylinder is 7 cm. Find the volume and total surface area of the solid. (Take $$\pi = \dfrac{22}{7}$$)

The diameter of a metallic sphere is $$6$$ cm. The sphere is melted and drawn into a wire of uniform circular cross-section. If the length of the wire is $$36$$ m, find the radius of its cross-section.

The slant height of the frustrum of a cone is $$4$$ cm. If the perimeters of its circular bases be $$18$$ cm and $$6$$ cm, find the curved surface area of the frustum and also find the cost of painting its total surface at the rate of Rs. $$12.50$$ per $$100 cm^{2}$$.

The radii of the circular ends of the frustum of a right circular cone are $$14$$ cm and $$12$$ cm and its thickness is $$9$$ cm. Find the lateral surface of the frustum. (Take $$\pi$$ $$= 3.14$$)

A rectangular tank $$28\ m$$ long and $$22\ m$$ wide is required to receive entire water from a full cylindrical tank of internal diameter $$28\ m$$ and depth $$4\ m.$$ Find the least height of the tank that will serve the purpose. $$\bigg($$Take $$\pi \ = \ \, \dfrac{22}{7}\bigg)$$

A godown building as shown in figure is made in the form of a cubical base with dimensions $$40m\, \times\, 14 m\, \times\, 4 m$$, surmounted by a half cylindrical curved roof having same length as that of the base. The diameter of the cylinder is $$14m$$. Find the volume of the building and its total outer surface area.

A cone is made from a circular sector of radius 2 units. If total surface area of cone (including base) is $$\displaystyle\pi $$ sq. units, find the radius of base of the cone 

A reservoir is in the shape of a frustum of a right circular cone It is $$8 \ m$$ across at the top and $$4\ m$$ across at the bottom. If it is $$6\ m$$ deep its capacity is