A solid sphere and a solid hemisphere have the same total surface area. The ratio of their volumes is 

The four walls and ceiling of a room of length 25 m, breadth 12 m and height 10 m are to be painted. Painter A can paint 200 m2 in 5 days, Painter B can paint 250 m2 in 2 days. If A and B work together, they will finish the job in

• 6 days

• 
• 
• 

The external and the internal radii of a hollow right circular cylinder of height 15 cm are 6.75 cm and 5.25 cm respectively. If it is melted to form a solid cylinder of height half of the original cylinder, then the radius of the solid cylinder is

• 6 cm

• 6.5 cm

• 7 cm

• 7 cm

A right circular cylinder is partially filled with water. Two iron spherical balls are completely immersed in the water so that the height of the water in the cylinder rises by 4 cm. If the radius of one ball is half of the other and the diameter of the cylinder is 18 cm, then the radii of the spherical balls are

• 6 cm and 12 cm

• 4 cm and 8 cm

• 3 cm and 6 cm

• 3 cm and 6 cm

The base of a right prism is a trapezium whose the length of parallel sides are 25 cm and 11 cm and the perpendicular distance between the parallel sides in 16 cm. If the height of the prism is 10 cm, then the volume of the prism is

• 1440 cu.cm

• 1540 cu.cm

• 2880 cu.cm

• 2880 cu.cm

If a cone is divided into two parts by drawing a plane through the midpoints of its axis, then the ratio of the volume of the two parts of the cone is

• 1 : 2

• 1 : 4

• 1 : 7

• 1 : 7

The whole surface area of a pyramid whose base is a regular polygon is 340 cm² and area of its base is 100 cm². Area of each lateral surface face is 30 cm². Then the number of lateral faces is

• 8

• 9

• 7

• 7

From a solid right circular cylinder of length 4 cm and diameter 6 cm, a conical cavity of the same height and base is hollowed out. The whole surface area of the remaining solid (in square cm) is

• 48 π

• 15 π

• 63 π

• 53 π

A spherical ball of radius 1 cm is dropped into a conical vessel of radius 3 cm and slant height 6 cm. The volume of water (in cm³), that can just immerse the ball, is

Assume that a drop of water is spherical and its diameter is one-tenth of a cm. A conical glass has a height equal to the diameter of its rim. If 32000 drops of water fill the glass completely, then the height of the glass (in cm) is

• 3

• 1

• 4

• 4