Area And Volume...

A metallic right circular cone of height 18 cm and base radius 7 cm is melted into a cuboid whose two sides measure 11 cm and 6 cm. What is the length of the third side of the cuboid?

A cylindrical vessel of diameter 4 cm is partly filled with water. In the vessel, 300 lead balls are dropped. The rise in the water level is 2.7 cm. The diameter of each ball is

A hemisphere of inner diameter 9 cm is completely filled with a liquid. This is to be poured into cylindrical bottles of diameter 3 cm and height 2 cm. The number of bottles required is

From a circle of radius 15 cm, a sector with 288⁰ angle is cut out and its bounding radii are bent so as to form a cone. What is its approximate volume?

If one cubic centimetre of cast iron weighs 21 g, then the mass of a cast iron pipe of length 1 m with a bore of 3 cm and thickness of 1 cm is

Water flows through a cylindrical pipe of inner diameter 7 cm at 192.5 litres per minute. Find the rate of flow (in kilometres per hour). [1 litre = 1 dm³]

A hemispherical bowl is made up of steel of 0.25 cm thickness. The inner radius of the bowl is 5 cm. The volume of steel used is

If the radii of the circular ends of a conical bucket are 28 cm and 7 cm and the height is 21 cm, then the capacity of the bucket is

What is the radius of a cylinder whose lateral surface area is 704 cm² and height is 4 cm?

A toy is of the shape of a cone over a hemisphere. The radius of the hemisphere is 3 cm. The total height of the toy is 7 cm. What is the total area of the toy?

A cone is divided into two parts by drawing a plane through the mid-point of its axis, parallel to its base. Compare the volumes of the two parts.

A toy is made in the form of a hemisphere surmounted by a right circular cone, whose circular base coincides with the plane surface of the hemisphere. The base radius of the cone is 3.5 m and its volume is 2/3 of the volume of the hemisphere. Calculate the total height of conical part.

The diameter of a copper sphere is 8 cm. It is beaten and drawn into a wire of diameter 0.2 cm. The length of the wire is

The radius of a cylinder is doubled but its lateral surface area is unchanged. Then, how will its height be affected?

A cylindrical rod, whose height is 16 times of its radius, is melted and recast into spherical balls of same radius. The number of balls will be

A hollow sphere of internal and external diameters 4 cm and 8 cm respectively, is melted into a cone of base diameter 16 cm. Find the height of the cone.

A hollow garden roller, 63 cm wide with a girth of 440 cm is made of iron of thickness 4 cm. The volume of the iron used is

A cylinder, a hemisphere and a cone stand on the same base and have equal heights. The ratio of the areas of their curved surfaces is

The radius of a sphere is increased by k%. Its surface area increases by

Vertical and horizontal cross-sections of a right circular cylinder are always ______ and ______ respectively.