## MENSURATION

### Solved Question Papers

Q.In a right angled triangle, find the hypotenuse if base and perpendicular are respectively 36015 cm and 48020 cm.

1.69125 cm
2.60025 cm
3.391025 cm
4.60125 cm

Q.The perimeter of an equilateral triangle is 723–√ cm. Find its height.

1.63
2.24
3.18
4.36

Q.The inner circumference of a circular track is 440 cm. The track is 14 cm wide. Find the diameter of the outer circle of the track.

1.84 cm
2.168 cm
3.336 cm
4.77 cm

Q.A race track is in the form of a ring whose inner and outer circumference are 352 metre and 396 metre respectively. Find the width of the track.

1.7
2.14
3.14pi
4.7pi

Q.The outer circumference of a circular track is 220 metre. The track is 7 metre wide everywhere. Calculate the cost of levelling the track at the rate of 50 paise per square metre.

1.1556.5
2.3113
3.593
4.693

Q.Find the area of a quadrant of a circle in cm2 whose circumference is 44 cm

1.77
2.38.5
3.19.25
4.19.25pi

Q.A pit 7.5 metre long, 6 metre wide and 1.5 metre deep is dug in a field. Find the volume of soil in m3 removed in cubic metres

1.135
2.101.25
3.50.625
4.67.5

Q.Find the length of the longest pole that can be placed in an indoor stadium 24 metre long, 18 metre wide and 16 metre high

1.30 metres
2.25 metres
3.34 metres
4.√580

Q.The length, breadth and height of a room are in the ratio of 3 : 2 : 1. If its volume be 1296 m3 , find its breadth

1.18 metres
2.18 metres
3.16 metres
4.12 metres

Q.The volume of a cube is 216 cm3 . Part of this cube is then melted to form a cylinder of length 8 cm. Find the volume of the cylinder in cm3

1.342
2.216
3.36
4.data insufficient

Q.The whole surface of a rectangular block is 8788 square cm. If length, breadth and height are in the ratio of 4 : 3 : 2, find length. in cm

1.26 cm
2.52 cm
3.104 cm
4.13 cm

Q.Three metal cubes with edges 6 cm, 8 cm and 10 cm respectively are melted together and formed into a single cube. Find the side of the resulting cube in cm

1.11
2.12
3.13
4.24

Q.Find curved and total surface area of a conical flask of radius 6 cm and height 8 cm.

1.60p, 96p
2.20p, 96p
3.60p, 48p
4.30p, 48p

Q.The volume of a right circular cone is 100p cm3 and its height is 12 cm. Find its curved surface area in cm2

1.130 p
2.65 p
3.204 p
4.65

Q.The diameters of two cones are equal. If their slant height be in the ratio 5 : 7, find the ratio of their curved surface areas

1.25 : 7
2.25 : 49
3.5 : 49
4.5 : 7

Q.The curved surface area of a cone is 2376 square cm and its slant height is 18 cm. Find the diameter.

1.6 cm
2.18 cm
3.84 cm
4.12 cm

Q.
The ratio of radii of a cylinder to a that of a cone is 1 : 2. If their heights are equal, find the ratio of their volumes?

1.1 : 3
2.2 : 3
3.3 : 4
4.3 : 1

Q.A silver wire when bent in the form of a square, encloses an area of 484 cm2 . Now if the same wire is bent to form a circle, the area of enclosed by it would be

1.308
2.196
3.616
4.88

Q.The circumference of a circle exceeds its diameter by 16.8 cm. Find the circumference of the circle

1.12.32 cm
2.49.28 cm
3.58.64 cm
4.24.64 cm

Q.A bicycle wheel makes 5000 revolutions in moving 11 km. What is the radius of the wheel?

1.70 cm
2.135 cm
3.17.5 cm
4.35 cm

Q.The volume of a right circular cone is 100p cm3 and its height is 12 cm. Find its slant height

1.13 cm
2.16 cm
3.9 cm
4.26 cm

Q.The short and the long hands of a clock are 4 cm and 6 cm long respectively. What will be sum of distances travelled by their tips in 4 days? (Take p = 3.14)

1.954.56 cm
2.3818.24 cm
3.2909.12 cm
4.2703.56 cm

Q.The surface areas of two spheres are in the ratio of 1 : 4. Find the ratio of their volumes.

1.1 : 2
2.1 : 8
3.1 : 4
4.2 : 1

Q.The outer and inner diameters of a spherical shell are 10 cm and 9 cm respectively. Find the volume of the metal contained in the shell. (Use p = 22/7) in cm3

1.6956
2.141.95
3.283.9
4.478.3

Q.The radii of two spheres are in the ratio of 1 : 2. Find the ratio of their surface areas

1.1 : 3
2.2 : 3
3.1 : 4
4.3 : 4

Q.A sphere of radius r has the same volume as that of a cone with a circular base of radius r. Find the height of cone

1.2r
2.r/3
3.4r
4.(2/3)r

Q.Find the number of bricks, each measuring 25 cm × 12.5 cm × 7.5 cm, required to construct a wall 12 m long, 5 m high and 0.25 m thick, while the sand and cement mixture occupies 5% of the total volume of wall.

1.6080
2.3040
3.1520
4.12160

Q.A road that is 7 m wide surrounds a circular path whose circumference is 352 m. What will be the area of the road in cm2?

1.2618
2.654.5
3.1309
4.5236

Q.In a shower, 10 cm of rain falls. What will be the volume of water that falls on 1 hectare area of ground in m3?

1.500
2.650
3.1000
4.750

Q.Seven equal cubes each of side 5 cm are joined end to end. Find the surface area of the resulting cuboid in cm2.

1.750
2.1500
3.2250
4.700

Q.In a swimming pool measuring 90 m by 40 m, 150 men take a dip. If the average displacement of water by a man is 8 cubic metres, what will be rise in water level?

1.30 cm
2.50 cm
3.20 cm
4.33.33 cm

Q.How many metres of cloth 5 m wide will be required to make a conical tent, the radius of whose base is 7 m and height is 24 m

1.55 m
2.330 m
3.220 m
4.110 m

Q.Two cones have their heights in the ratio 1 : 2 and the diameters of their bases are in the ratio 2 : 1. What will be the ratio of their volumes?

1.4 : 1
2.2 : 1
3.3 : 2
4.1 : 1

Q.A conical tent is to accommodate 10 persons. Each person must have 6 m2 space to sit and 30 m3 of air to breath. What will be the height of the cone?

1.37.5 m
2.150 m
3.75 m
4.None of these

Q.A closed wooden box measures externally 10 cm long, 8 cm broad and 6 cm high. Thickness of wood is 0.5 cm. Find the volume of wood used. in cm3

1.230
2.165
3.330
4.300

Q.A cuboid of dimension 24 cm × 9 cm × 8 cm is melted and smaller cubes are of side 3 cm is formed. Find how many such cubes can be formed.

1.27
2.64
3.54
4.32

Q.Three cubes each of volume of 216 m3 are joined end to end. Find the surface area of the resulting figure. in m2

1.504
2.216
3.432
4.480

Q.A hollow spherical shell is made of a metal of density 4.9 g/cm3 . If its internal and external radii are 10 cm and 12 cm respectively, find the weight of the shell. (Take p = 3.1416)

1.5016 gm
2.1416.8 gm
3.14942.28 gm
4.5667.1 gm

Q.The largest cone is formed at the base of a cube of side measuring 7 cm. Find the ratio of volume of cone to cube.

1.20 : 21
2.22 : 21
3.21 : 22
4.42 : 11

Q.A spherical cannon ball, 28 cm in diameter, is melted and cast into a right circular conical mould the base of which is 35 cm in diameter. Find the height of the cone correct up to two places of decimals.

1.8.96 cm
2.35.84 cm
3.5.97 cm
4.17.92 cm

Q.Find the area of the circle circumscribed about a square each side of which is 10 cm in cm3

1.314.28
2.157.14
3.150.38
4.78.57

Q.Find the radius of the circle inscribed in a triangle whose sides are 8 cm, 15 cm and 17 cm

1.4 cm
2.5 cm
3.3 cm
4.2√2