- Area (total surface and curved surface) and Volume
- Direct application problems including cost, Inner and Outer volume and melting and recasting method to find the volume or surface area of a new solid.
- Frustum is not included.
- Areas of sectors of circles other than quartercircle and semicircle are not included
A heap of wheat is in the form of a cone of diameter 16.8 m and height 3.5 m. Find its volume. How much cloth is required to just cover the heap?
A solid metallic hemisphere of diameter 28 cm is melted and recast into a number of identical solid cones, each of diameter 14 cm and height 8 cm. find the number of cones so formed.
A hemispherical bowl of diameter 7.2 cm is filled completely with chocolate sauce. This sauce is poured into a inverted cone of radius 4.8 cm. Find the height of the cone is it is completely filled.
The horizontal cross-section of a water tank is in the shape of a rectangle with semi-circle at one end, as shown in the following figure. The water is 2.4 metres deep in the tank. Calculate the volume of water in the tank in gallons.
A vessel, in the form of an inverted cone, is filled with water to brim. Its height is 32 cm and diameter of the base is 25.2 cm. Six equal solid cones are dropped in it, so that they are fully submerged. As a result one fourth of water is volume of each of the solid cone submerged?
The internal and external diameter of a hollow hemispherical vessel are 21 cm and 28 cm
(i) internal curved surface area
(ii) external curved surface area
(iii) total surface area
(iv) volume of material of the vessel
A solid sphere and a solid hemi-sphere have the same total surface area. Find the ratio between their volumes.