Mensuration Exercise 3

The water from a roof, 9 sq metres in area, flows down to a cylinder container of 900 cm² base. To what height will the water rise in cylinder if there is a rainfall of 0.1 mm?

The trunk of a tree is a right cylinder 1.5 m in radius and 10 m high. The volume of the timber which remains when the trunk is trimmed just enough to reduce it to a rectangular parallelepiped on a square base is

The capacity of a cylindrical tank is 246.4 litres. If the height is 4 metres, what is the diameter of the base?

A monument has 50 cylindrical pillars each of diameter 50 cm and height 4 m. What will be the labour charges for getting these pillars cleaned at the rate of 50 paise per sq. m? [use π = 3.14].

A cylindrical bucket of height 36 cm and radius 21 cm is filled with sand. The bucket is emptied on the ground and a conical heap of sand is formed, the height of the heap being 12 cm. The radius of the heap at the base is:

A conical vessel, whose internal radius is 12 cm and height 50 cm, is full of liquid. The contents are emptied into a cylindrical vessel with internal radius 10 cm. Find the height to which the liquid rises in the cylindrical vessel.

A right circular cone and a right circular cylinder have equal base and equal height. If the radius of the base and the height are in the ratio 5: 12, then the ratio of the total surface area of the cylinder to that of the cone is

A cone of height 9 cm with diameter of its base 18 cm is carved out from a wooden solid sphere of radius 9 cm. The percentage of the wood wasted is:

A conical vessel of base radius 2 cm and height 3 cm is filled with kerosene. This liquid leaks through a hole in the bottom and collects in a cylindrical jar of radius 2 cm. The kerosene level in the jar is

If the volume of a sphere is divided by its surface area, the result is 27 cms. The radius of the sphere is

A cylinder is circumscribed about a hemisphere and a cone is inscribed in the cylinder so as to have its vertex at the centre of one end, and the other end as its base. The volume of the cylinder, hemisphere and the cone are, respectively in the ratio:

A copper sphere of radius 3 cm is beaten and drawn into a wire of diameter 0.2 cm. The length of the wire is

A spherical ball of lead, 3 cm in diameter, is melted and recast into three spherical balls. The diameter of two of these balls are 1.5 cm and 2 cm respectively. The diameter of the third ball is

If the radius of a sphere is increased by 2 cm, then its surface area increases by 352 cm². The radius of the sphere before the increase was:

A rectangular tank measuring 5m × 4.5 m × 2.1 m is dug in the centre of the field measuring 13.5 m × 2.5. The earth dug out is spread evenly over the remaining portion of a field. How much is the level of the field raised?

A metal cube of edge 12 cm is melted and formed into three smaller cubes. If the edges of two smaller cubes are 6 cm and 8 cm, then find the edge of the third smaller cube.

The surface area of a cube is 150 m². The length of its diagonal is

The length of the longest rod that can be placed in a room which is 12 m long, 9 m broad and 8 m high is:

The volume of water measured on a rectangular field 500 m × 300 m is 3000 m³. Find the depth (amount) of rain that has fallen.

A cistern 6 m long and 4 m wide contains water up to a depth of 1 m 25 cm. The total area of the wet surface is:

The internal measurements of a box with lid are 115 × 75 × 35 cm³ and the wood of which it is made is 2.5 cm thick. Find the volume of wood.

A rectangular tank is 225 m by 162 m at the base. With what speed must water flow into it through an aperture 60 cm by 45 cm that the level may be raised 20 cm in 5 hours?

A cuboidal block of 6 cm × 9 cm × 12 cm is cut up into an exact number of equal cubes. The least possible number of cubes will be:

A wooden box of dimensions 8m × 7m × 6m is to carry rectangular boxes of dimensions 8 cm × 7 cm × 6cm. The maximum number of boxes that can be carried in the wooden box is

The ratio of height of a room to its semi-perimeter is 2: 5. It costs ₹260 to paper the walls of the room with paper 50 cm wide at ₹2 per metre allowing an area of 15 sq. m for doors and windows. The height of the room is:

The length, breadth and height of a cuboid are in the ratio 1: 2: 3. The length, breadth and height of the cuboid are increased by 100%, 200% and 200%, respectively. Then, the increase in the volume of the cuboid will be:

Water flows into a tank 200 m × 150 m through a rectangular pipe 1.5 m × 1.25 m @ 20 kmph. In what time (in minutes) will the water rise by 2 metres?

A metallic sheets is of rectangular shape with dimensions 48 cm × 36 cm. From each one of its corners, a square of 8 cm is cut off. An open box is made of the remaining sheet. Find the volume of the box

A cube of 384 cm² surface area is melt to make x number of small cubes each of 96 mm² surface area. The value of x is

It is required to fix a pipe such that water flowing through it at a speed of 7 metres per minute fills a tank of capacity 440 cubic metres in 10 minutes. The inner radius of the pipe should be:

A cylinder is filled to 4/5th its volume. It is then filled so that the level of water coincides with one edge of its bottom and top edge of the opposite side, In the process, 30 cc of the water is spilled. What is the volume of the cylinder?

A cylindrical container of radius 6 cm and height 15 cm is filled with ice-cream. The whole ice-cream has to be distributed to 10 children in equal cones with hemispherical tops. If the height of the conical portion is four times the radius of its base, then find the radius of the ice-cream cone.

A hemispherical bowl is filled to the brim with a beverage. The contents of the bowl are transfered into a cylindrical vessel whose radius is 50% more than its height. If the diameter is same for both the bowl and the cylinder, the volume of the beverage in the cylindrical vessel is: (i.e., some liquid will be left in the bowl.)

An ice-cream company makes a popular brand of ice-cream in rectangular shaped bar 6 cm long, 5 cm wide and 2 cm thick. To cut the cost, the company has decided to reduce the volume of the bar by 20%, the thickness remaining the same, but the length and width will be decreased by the same percentage amount. The new length L will satisfy:

If the radius of a circle is diminished by 10%, the area is diminished by

The length of a rectangular plot is increased by 25%. To keep its area unchanged, the width of the plot should be: