# Mensuration

### If the perimeter of a rectangle is 10 cm and the area is 4 cm^2

If the perimeter of a rectangle is 10 cm and the area is 4 cm2, then its length is

1. 6 cm
2. 5 cm
3. 4.5 cm
4. 4 cm

### A ball of radius 1 cm is put into a cylindrical pipe so that it fits inside the pipe

A ball of radius 1 cm is put into a cylindrical pipe so that it fits inside the pipe. If the length of the pipe is 14 m, what is the surface area of the pipe?

1. 2200 square cm
2. 4400 square cm
3. 8800 square cm
4. 17600 square cm

### Three circles each of radius 3.5 cm touch one another

Three circles each of radius 3.5 cm touch one another. The area subtended between them is

1. 6(√3π - 2) square units
2. 6(2π - √3) square units
3. 49/8 (2√3 - π) square units
4. 49/8 (√3 - π) square units 8

### The area of a regular hexagon of side 'a' is equal to

The area of a regular hexagon of side 'a' is equal to

1. √2/3 a2 square units
2. 3√3/2 a2 square units
3. 1/3 a2 square units
4. √3/2 a2 square units

### If the radius of a right circular cone is increased by p%

If the radius of a right circular cone is increased by p% without increasing its height, then what is the percentage increase in the volume of the cone?

1. p2
2. 2p2
3. p2/100
4. p(2 + p/100)

### A copper wire when bent in the form of a square encloses an area of 121 cm^2

A copper wire when bent in the form of a square encloses an area of 121 cm2. If the same wire is bent in the form of a circle, it encloses an area equal to

1. 121 cm2
2. 144 cm2
3. 154 cm2
4. 168 cm2

### If the surface area of a sphere is reduced to one-ninth of the area

If the surface area of a sphere is reduced to one-ninth of the area, its radius reduces to

1. One-fourth
2. One-third
3. One-fifth
4. One-ninth

### In a trapezium ABCD, AB is parallel to CD and the diagonals

In a trapezium ABCD, AB is parallel to CD and the diagonals intersect each other at O. What is the ratio of OA to OC equal to?

1. Ratio of OB to OD
2. Ratio of BC to CD
3. Ratio of AD to AB
4. Ratio of AC to BD

### Ice-cream, completely filled in a cylinder of diameter 35 cm and height 32 cm

Ice-cream, completely filled in a cylinder of diameter 35 cm and height 32 cm, is to be served by completely filling identical disposable cones of diameter 4 cm and height 7 cm. The maximum number of persons that can be served in this way is

1. 950
2. 1000
3. 1050
4. 1100

### The radius of a circle is increased so that its circumference increases by 15%

The radius of a circle is increased so that its circumference increases by 15%. The area of the circle will increase by

1. 31.25%
2. 32.25%
3. 33.25%
4. 34.25%

### ABCD is a rectangle. The diagonals AC and BD intersect at O

ABCD is a rectangle. The diagonals AC and BD intersect at O. If AB = 32 cm and AD = 24 cm, then what is OD equal to?

1. 22 cm
2. 20 cm
3. 18 cm
4. 16 cm

### A field is divided into four regions. What is the area of the field

A field is divided into four regions as shown in the given figure. What is the area of the field in square metres? 1. 6 + 3√5/4
2. 5 + 3√3/2
3. 9 + 3√15/4
4. 7 + 2√2

### D is the diameter of each circle. What is the diameter of the shaded circle

In the figure given below, D is the diameter of each circle. What is the diameter of the shaded circle? 1. D(√2 - 1)
2. D(√2 + 1)
3. D(√2 + 2)
4. D(2 - √2)

### AC is parallel to ED and AB = DE = 5 cm and BC = 7 cm

In the figure given below, AC is parallel to ED and AB = DE = 5 cm and BC = 7 cm. What is the area ABDE : area BDE : area BCD equal to? 1. 10 : 5 : 7
2. 8 : 4 : 7
3. 2 : 1 : 2
4. 8 : 4 : 5

### What is the number of wax balls, each of radius 1 cm

What is the number of wax balls, each of radius 1 cm, that can be molded out of a sphere of radius 8 cm?

1. 1024
2. 768
3. 512
4. 256

### The diameter of a metallic sphere is 6 cm

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, then what is its radius equal to?

1. 0.001 cm
2. 0.01 cm
3. 0.1 cm
4. 1.0 cm

### The total outer surface area of a right circular cone of height 24 cm

The total outer surface area of a right circular cone of height 24 cm with a hemisphere of radius 7 cm upon its base is

1. 327 π
2. 307 π
3. 293 π
4. 273 π

### The radius of a sphere is equal to the radius of the base of a right circular cone

The radius of a sphere is equal to the radius of the base of a right circular cone, and the volume of the sphere is double the volume of the cone. The ratio of the height of the cone to the radius of its base is

1. 3 : 2
2. 1 : 2
3. 2 : 1
4. 2 : 3

### If the height of a right circular cone is increased by 200%

If the height of a right circular cone is increased by 200%, and the radius of the base is reduced by 50%, then the volume of the cone

1. remains unaltered
2. decreases by 25%
3. increases by 50%
4. increases by 25%

### A cylindrical vessel of radius 4 cm contains water

A cylindrical vessel of radius 4 cm contains water. A solid sphere of radius 3 cm is lowered into the water until it is completely immersed. The water level in the vessel will rise by

1. 4.5 cm
2. 2.25 cm
3. 2 cm
4. 1.5 cm

### 10 cylindrical pillars of a building have to be painted

10 cylindrical pillars of a building have to be painted. The diameter of each pillar is 70 cm and the height is 4 m. What is the cost of painting at the rate of Rs.5 per square metre?

1. Rs.400
2. Rs.440
3. Rs.480
4. Rs.500

### If three metallic spheres of radii 6 cm, 8 cm, and 10 cm are melted

If three metallic spheres of radii 6 cm, 8 cm, and 10 cm are melted to form a single sphere, then the diameter of the new sphere will be

1. 12 cm
2. 24 cm
3. 30 cm
4. 36 cm

### A wall is of the form of a trapezium with height 4 m

A wall is of the form of a trapezium with height 4 m and parallel sides being 3 m and 5 m. What is the cost of painting the wall, if the rate of painting is Rs.25/- per square metre?

1. Rs.800
2. Rs.480
3. Rs.400
4. Rs.240

### A gardener has 1000 plants. He wants to plant them in such a way

A gardener has 1000 plants. He wants to plant them in such a way that the number of rows and the number of columns remains the same. What is the minimum number of plants that he needs more for this purpose?

1. 34
2. 24
3. 32
4. 14

### A village having a population of 4000 requires 150 litres of water

A village having a population of 4000 requires 150 litres of water per head per day. It has a tank measuring 20 m x 15 m x 6 m. The water of this tank will last for

1. 3 days
2. 2 days
3. 4 days
4. 5 days

### The areas of two circular fields are in the ratio 16 : 49

The areas of two circular fields are in the ratio 16 : 49. If the radius of the bigger field is 14 m, then what is the radius of the smaller field?

1. 4 m
2. 8 m
3. 9 m
4. 10 m

### If each of the dimensions of a rectangle is increased by 200%

If each of the dimensions of a rectangle is increased by 200%, the area is increased by

1. 300%
2. 400%
3. 600%
4. 800%

### The radius of the base of a right circular cone is increased by 15%

The radius of the base of a right circular cone is increased by 15% keeping the height fixed. The volume of the cone will be increased by

1. 34.75%
2. 32.25%
3. 31%
4. 30%

### A right circular cone, of height 12 ft, stands on its base

A right circular cone, of height 12 ft, stands on its base which has diameter 8 ft. The tip of the cone is cut off with a plane which is parallel to the base and 9 ft from the base. With π = 22/7, the volume, in cubic ft, of the remaining part of the cone is

### The surface area of a sphere is 616 square cm

The surface area of a sphere is 616 square cm. If its radius is changed so that the area gets reduced 75% then the radius becomes

1. 1.6 cm
2. 2.3 cm
3. 2.5 cm
4. 3.5 cm

### 50 men took a dip in a water tank 40 m long and 20 m broad on a religious day

50 men took a dip in a water tank 40 m long and 20 m broad on a religious day. If the average displacement of water by a man is 4 m3, then the rise in the water level in the tank will be

1. 20 cm
2. 25 cm
3. 35 cm
4. 50 cm

### A metallic sheet is of rectangular shape with dimensions 48 m x 36 m. From each of its corners

A metallic sheet is of rectangular shape with dimensions 48 m x 36 m. From each of its corners, a square is cut off so as to make an open box. If the length of the square is 8 m, the volume of the box (in m3) is

1. 8960
2. 5120
3. 4830
4. 6420

### A right circular cone, a right circular cylinder and a hemisphere, all have the same radius

A right circular cone, a right circular cylinder and a hemisphere, all have the same radius, and the heights of cone and cylinder equal their diameters. Then their volumes are proportional, respectively to

1. 2 : 1 : 3
2. 3 : 2 : 1
3. 1 : 2 : 3
4. 1 : 3 : 1

### A slab of ice 8 inches in length, 11 inches in breadth, and 2 inches thick was melted

A slab of ice 8 inches in length, 11 inches in breadth, and 2 inches thick was melted and re-solidified into the form of a rod of 8 inches diameter. The length of such a rod, in inches, is nearest to

1. 3
2. 3.5
3. 3
4. 4.5

### A right circular cone of height h is cut by a plane parallel to the base and at a distance h/3

A right circular cone of height h is cut by a plane parallel to the base and at a distance h/3 from the base, then the volumes of the resulting cone and the frustum are in the ratio

1. 1 : 4
2. 1 : 7
3. 8 : 19
4. 1 : 3

### In a rectangle, the difference between the sum of the adjacent sides and the diagonal is half the length

In a rectangle, the difference between the sum of the adjacent sides and the diagonal is half the length of the longer side. What is the ratio of the shorter to the longer side?

1. 2 : 5
2. √3 : 2
3. 3 : 4
4. 1 : √3

### Four horses are tethered at four corners of a square plot of side 14 m

Four horses are tethered at four corners of a square plot of side 14 m so that the adjacent horses can just reach one another. There is a small circular pond of area 20 m2 at the centre. Find the ungrazed area.

1. 168 m2
2. 84 m2
3. 42 m2
4. 22 m2

### From a circular sheet of paper with a radius 20 cm, four circles of radius 5 cm each are cut out

From a circular sheet of paper with a radius 20 cm, four circles of radius 5 cm each are cut out. What is the ratio of the uncut to the cut portion?

1. 4 : 3
2. 4 : 1
3. 3 : 1
4. 1 : 3

### In a triangle ABC, the lengths of the sides AB and AC equal 17.5 cm and 9 cm respectively

In a triangle ABC, the lengths of the sides AB and AC equal 17.5 cm and 9 cm respectively. Let D be a point on the line segment BC such that AD is perpendicular to BC. If AD = 3 cm, then what is the radius (in cm) of the circle circumscribing the triangle ABC?

1. 17.05
2. 22.45
3. 26.25
4. 27.85

### If a right circular cylinder of height 14 is inscribed in a sphere of radius 8

If a right circular cylinder of height 14 is inscribed in a sphere of radius 8, then the volume of the cylinder is

1. 110
2. 220
3. 440
4. 660

### Let ABCDEF be a regular hexagon with each side of length 1 cm

Let ABCDEF be a regular hexagon with each side of length 1 cm. The area (in sq cm) of a square with AC as one side is

1. 3√2
2. 3
3. 4
4. √3

### The base of a vertical pillar with uniform cross section is a trapezium

The base of a vertical pillar with uniform cross section is a trapezium whose parallel sides are of lengths 10 cm and 20 cm while the other two sides are of equal length. The perpendicular distance between the parallel sides of the trapezium is 12 cm. If the height of the pillar is 20 cm, then the total area, in sq cm, of all six surfaces of the pillar is

1. 1300
2. 1340
3. 1480
4. 1520