TS 10th Class Maths Bits Chapter 10 Mensuration

Solving these TS 10th Class Maths Bits with Answers Chapter 10 Mensuration Bits for 10th Class will help students to build their problem-solving skills.

Mensuration Bits for 10th Class

Question 1.
To find out quantity of water in the bottle, we measure
A) surface area
B) total surface area
C) volume
D) base area
Answer:
C) volume

Question 2.
Lateral surface area of a cube is given by
A) 2a²
B) 4a²
C) 6a²
D) a³
Answer:
B) 4a²

Question 3.
Total surface area of a regular circular cylinder is
A) 2πrh
B) πrl
C) 2πr(π + r)
D) 2πr(r + h)
Answer:
D) 2πr(r + h)

Question 4.
The ratio of volumes of a cone and a cylinder whose radii and height are equal is ………………….
A) 3 : 1
B) 1 : 3
C) 1 : 2
D) 1 : 1
Answer:
B) 1 : 3

Question 5.
The diagonal of a cube whose side is ‘a’ units is ……………..
A) a
B) \(\sqrt{2}\) a
C) \(\sqrt{3}\) a
D) 2a
Answer:
C) \(\sqrt{3}\) a

Question 6.
The volume of a sphere of radius ‘r’ is obtained by multiplying its surface area by
A) 4/3
B) r/3
C) 4r/3
D) 3r
Answer:
B) r/3

Question 7.
The total surface area of a solid hemisphere of radius 7cm is
A) 239 π cm²
B) 449 π cm²
C) 221 π cm²
D) 129 π cm²
Answer:
A) 239 π cm²

Question 8.
The curved surface area of a right circular cone of height 15cm and base diameter 16cm is.
A) 144 π cm²
B) 136 π cm²
C) 105 π cm²
D) 120 π cm²
Answer:
B) 136 π cm²

Question 9.
The surface areas of two spheres are in the ratio 1 : 4 then, ratio of their volumes is
A) 1 : 4
B) 2 : 8
C) 1 : 16
D) 1 : 64
Answer:
A) 1 : 4

Question 10.
The volume of the largest right circular cone that can be cut out from a cube of edge 4.2 cm is
A) 19.4 cm³
B) 74.6 cm³
C) 9.7 cm³
D) 8.4 cm³
Answer:
A) 19.4 cm³

Question 11.
The ratio of volume of cone and cylinder of equal diameter and height
A) 3 : 1
B) 1 : 2
C) 2 : 1
D) 1 : 3
Answer:
D) 1 : 3

Question 12.
An iron cylindrical rod has a height 4 times of its radius is melted and cast into spherical balls of the same radius. The number of balls cast is
A) 4
B) 3
C) 2
D) 1
Answer:
D) 1

Question 13.
A cone and a hemi-sphere have equal bases and equal volumes then the ratio of their heights
A) 2 : 1
B) 3 : 1
C) 4 : 1
D) 1 : 1
Answer:
A) 2 : 1

Question 14.
The volume of the greatest cylinder that can be cut form a solid wooden cube of length of edge 14cm is
A) 2156 cm³
B) 1078 cm³
C) 539 cm³
D) 428 cm³
Answer:
A) 2156 cm³

Question 15.
A shuttle cock is a combination of
A) cylinder, sphere
B) sphere, cone
C) cylinder, hemisphere
D) hemisphere, first term cone
Answer:
D) hemisphere, first term cone

Question 16.
T.S.A of a solid hemisphere whose radius is 7cm is …………….. cm².
A) 327 π
B) 144 π
C) 147 π
D) 189 π
Answer:
C) 147 π

Question 17.
If the radius of base of a cylinder is doubled and the height remains unchanged, it’s C.S.A becomes
A) double
B) times
C) half
D) no change
Answer:
A) double

Question 18.
The number of cubes of side 2cm which can be cut from a cube of side 6 cm is
A) 3
B) 18
C) 27
D) 9
Answer:
C) 27

Question 19.
If the diameter of a sphere is’d’ then its volume is
A) \(\frac{1}{6}\) πd³
B) \(\frac{4}{3}\) πd³
C) \(\frac{1}{24}\) πd³
D) \(\frac{1}{3}\) πd³
Answer:
A) \(\frac{1}{6}\) πd³

Question 20.
A cylindrical, a cone and a hemisphere are of equal base and have the same height, then the ratio of their volumes is
A) 3 : 1 : 1
B) 3 : 2 : 1
C) 1 : 2 : 3
D) 1 : 3 : 2
Answer:
A) 3 : 1 : 1

Question 21.
Total surface area of a cube is 216 cm² then its volume is ……………….. cm³.
A) 216
B) 196
C) 212
D) 144
Answer:
A) 216

Question 22.
The total surface area of a cube is 54 cm² then its side is ………………. cm. (A.P. Mar. ’15 )
A) 6
B) 9
C) 12
D) 3
Answer:
D) 3

Question 23.
Base area of a regular cylinder is 154 cm² then its radius is ……………….. (A.P. Mar. ’16, ’15)
A) 49 cm
B) 7 cm
C) 22 cm
D) 14 cm
Answer:
B) 7 cm

Question 24.
If the height and radius of a cone are 1.5 and 8 cm then its slant height = ………………. cm
A) 2.5 cm
B) 7.5 cm
C) 5 cm
D) 10 cm
Answer:
C) 5 cm

Question 25.
Curved surface area of a hemi-sphere = ………………. (A.P. Mar. ’15)
A) πr²
B) \(\frac{1}{3}\)πr²
C) 3πr²
D) 2πr²
Answer:
D) 2πr²

Question 26.
Volume of a cube having 1 cm side is ……………….. (A.P. Mar. ’16, June ’15)
A) 1 cm³
B) 3 cm³
C) 1 cm²
D) 3 cm²
Answer:
A) 1 cm³

Question 27.
Ratio of volumes of two spheres is 8 : 27 then ratio of their curved surface areas is …………….. (A.P. June ’15)
A) 2 : 3
B) 4 : 27
C) 8 : 9
D) 4 : 9
Answer:
C) 8 : 9

Question 28.
Football is in a model of …………………. (A.P. Mar. ’16)
A) circle
B) cylinder
C) Sphere
D) cone
Answer:
C) Sphere

Question 29.
Radius of a cone is ‘r’, height is ‘h’ and its slant height is 7 then which of the following is false ? (A.P. Mar. ’16)
A) always l > h
B) always l > r
C) always r > p
D) l² = r² + h²
Answer:
C) always r > p

Question 30.
Radius, height, slant height of a cone are| r, h, l, then ‘l’ value in terms of r and h is ……………… (T.S. Mar. ’15)
A) \(\sqrt{h^2-r^2}\)
B) \(\sqrt{r^2+h^2}\)
C) \(\sqrt{r^2-h^2}\)
D) \(\sqrt{4 r^2+h^2}\)
Answer:
B) \(\sqrt{r^2+h^2}\)

Question 31.
To calculate the quantity of milk inside a bottle, we need to find out
A) Area
B) Volume
C) Density
D) TSA
Answer:
B) Volume

Question 32.
Sphere, cylinder and cone have same heights and radii, then its ratios of curved surface areas.
A) 4 : 4 : \(\sqrt{5}\)
B) 1 : 1 : \(\sqrt{5}\)
C) \(\sqrt{5}\) : 4 : 4
D) 4 : \(\sqrt{5}\) : 4
Answer:
A) 4 : 4 : \(\sqrt{5}\)

Question 33.
Diagonal of a cuboid is …………….. units.
A) \(\sqrt{l^2+b^2+h^2}\)
B) \(1 \sqrt{\mathrm{b}^2+\mathrm{h}^2}\)
C) \(b \sqrt{h^2+r^2}\)
D) none
Answer:
A) \(\sqrt{l^2+b^2+h^2}\)

Question 34.
The radius of a conical tent is 3 meter and height is 4 meter then its slant height is …………………. meter.
A) 5
B) 725
C) A and B
D) none
Answer:
A) 5

Question 35.
The total surface area of a solid hemisphere of radius 1 unit is
A) 3πr²
B) 2πr²
C) 3π
D) 2π
Answer:
C) 3π

Question 36.
Volume of is cuboid.
A) 16
B) 10
C) 6
D) 12
Answer:
C) 6

Question 37.
The diameter of a metallic sphere is 6 cm and melted to draw a wire of diameter 2cm, then the length of the wire is
A) 48 cm
B) 12 cm
C) 36 cm
D) 24 cm
Answer:
C) 36 cm

Question 38.
A solid sphere of radius r melted and recast into the shape of a solid cone of height r, then radius of the base of the cone is (of equal volume)
A) 2r
B) r
C) 3r
D) 4r
Answer:
A) 2r

Question 39.
If the radii of circular ends of a frustum of a cone are 20 cm and 12 cm and its height is 6cm, then the slant height of the frustum is …………………. cm.
A) 10
B) 6
C) 9
D) 8
Answer:
A) 10

Question 40.
The number of balls, each of radius 1 cm that can be made from a solid sphere of radius 8 cm is
A) 64
B) 216
C) 16
D) 512
Answer:
D) 512

Question 41.
The ratio of volume of two cones is 4 : 5 and the ratio of the radii of their base is 2 : 3 then ratio of their vertical heights is
A) 4 : 5
B) 9 : 5
C) 3 : 5
D) 2 : 5
Answer:
B) 9 : 5

Question 42.
If the ratio of radii of two spheres is 2 : 3 then the ratio of their surface areas is
A) 3 : 2
B) 27 : 8
C) 8 : 27
D) 4 : 9
Answer:
D) 4 : 9

Question 43.
If a cone is cut into two parts by a horizontal plane passing through the mid point of the axis, the ratio of the volumes of the
upper part and the cone is
A) 1 : 2
B) 1 : 4
C) 1 : 6
D) 1 : 8
Answer:
D) 1 : 8

Question 44.
The height of a cylinder is doubled and radius is tripled then its curved surface area will become …………….. times.
A) 7
B) 6
C) 9
D) 12
Answer:
B) 6

Question 45.
Diameter of a sphere which can in-scribe a cube of edge x cm is ……………
A) \(\frac{x}{3}\)
B) \(\frac{x^2}{3}\)
C) \(\frac{x}{\sqrt{3}}\)
D) x\(\sqrt{3}\)
Answer:
D) x\(\sqrt{3}\)

Question 46.
Total surface area of hemisphere of radius r is ………….
A) πr²
B) 2πr²
C) 3πr²
D) none
Answer:
C) 3πr²

Question 47.
Volume of frustrum of a cone is
A) \(\frac{\pi h}{3}\) (R² + r²2 +R.r)
B) \(\frac{\mathrm{h}}{3}\)(R² + r²)
C) \(\frac{\pi h}{3}\)(R² +r²)
D) none
Answer:
A) \(\frac{\pi h}{3}\) (R² + r²2 +R.r)

Question 48.
If the length of each diagonal of a cube is doubled, then its volume become ………………. times.
A) 7
B) 8
C) 9
D) none
Answer:
B) 8

Question 49.
If a right angled triangle is revolved about its hypotenuse then it will form a ………………….
A) double cone
B) triple cone
C) only cone
D) none
Answer:
A) double cone

Question 50.
A solid sphere of radius 10 cm is moulded into 8 spherical solid balls of equal radius, then radius of small spherical balls is ……………… cm.
A) 10
B) 9
C) 6
D) 5
Answer:
D) 5

Question 51.
In a hollow cuboid box of size 4 × 3 × 2m, the number of solid iron spherical balls of radius 0.5 m that can be packed ……………
A) 71
B) 24
C) 22
D) 16
Answer:
B) 24

Question 52.
If the external and internal radii of a hollow hemispherical bowl are R and r, then its total surface area is ……………….
A) πr² + R²
B) πR² + r²
C) πR² + r
D) π(3R² + r²)
Answer:
D) π(3R² + r²)

Question 53.
Volume of cylinder is …………………. cu. units.
A) πr²h
B) πr²
C) \(\frac{\pi}{r}\)
D) none
Answer:
A) πr²h

Question 54.
Volume of cone is ……………… cu. units.
A) \(\frac{1}{7}\) πr²h
B) \(\frac{1}{2}\) πr²h
C) πr²h
D) \(\frac{1}{3}\) πr²h
Answer:
D) \(\frac{1}{3}\) πr²h

Question 55.
Volume of sphere is ………………… cu.units.
A) \(\frac{4}{3}\) πr²h
B) \(\frac{4}{3}\) πr³
C) \(\frac{1}{3}\) πr³
D) none
Answer:
B) \(\frac{4}{3}\) πr³

Question 56.
Volume of cuboid = …………………… cu.units
A) l²b
B) lbh²
C) lbh
D) none
Answer:
C) lbh

Question 57.
Total surface area of cone is …………………. sq.units.
A) πr² + πrl
B) πr² + πr
C) πr² + πl
D) none
Answer:
A) πr² + πrl

Question 58.
Total surface area of cylinder is ……………………. sq.units.
A) πrh + πr²
B) 2πr + π
C) 2πrh²
D) 2πrh + 2πr²
Answer:
D) 2πrh + 2πr²

Question 59.
Total surface area of hemisphere is ………………… sq.units.
A) \(\frac{\pi r^2}{\mathrm{~h}}\)
B) 4πr²
C) 8πr²h
D) none
Answer:
D) none

Question 60.
Surface area of sphere is ……………… sq.units.
A) \(\frac{\pi r^2}{\mathrm{~h}}\)
B) 4πr²
C) 8πr²h
D) none
Answer:
B) 4πr²

Question 61.
Volume of a cube is ………………… cu.units.
A) 3a³
B) a²h
C) a³
D) none
Answer:
C) a³

Question 62.
The volume of a cube is 216 cm3 then edge is ………………….. cm.
A) 9
B) 10
C) 16
D) 6
Answer:
D) 6

Question 63.
C.S.A of cone = ……………….. sq. units.
A) π²r²l
B) πrl²
C) πr²
D) πrl
Answer:
D) πrl

Question 64.
In a cone, r = 7 cm, h = 10 cm then l = ………………….. cm
A) 12.2
B) 9.2
C) 10.1
D) none
Answer:
A) 12.2

Question 65.
π = …………………
A) \(\frac{22}{7}\)
B) \(\frac{2}{7}\)
C) \(\frac{22}{3}\)
D) none
Answer:
A) \(\frac{22}{7}\)

Question 66.
The volume of a right circular cone with radius 6 cm and height 7 cm is …………………. cm³.
A) 462
B) 264
C) 486
D) none
Answer:
B) 264

Question 67.
A heap of rice is in the form of a cone of diameter 12 m and height 8 m then volume is ……………… m³.
A) 110.53
B) 301.71
C) 310.51
D) none
Answer:
B) 301.71

Question 68.
In a cylinder, r = 8 cm, h = 10 cm, CSA = …………………. cm³.
A) \(\frac{3520}{7}\)
B) \(\frac{1520}{9}\)
C) \(\frac{3310}{41}\)
D) none
Answer:
A) \(\frac{3520}{7}\)

Question 69.
In a hemisphere, r = 1.75 cm then CSA = ……………… cm².
A) 38.5
B) 48.5
C) 93.5
D) none
Answer:
A) 38.5

Question 70.
Volume of cone if r = 2 cm, h = 4 cm is ……………….
A) \(\frac{16}{3}\) π
B) \(\frac{6}{7}\) π
C) \(\frac{18}{31}\) π
D) none
Answer:
A) \(\frac{16}{3}\) π

Question 71.
Surface area of a sphere and cube are equal then the ratio of their volumes is …………………
A) \(\sqrt{\pi}\) : 1
B) \(\sqrt{\pi}\) : \(\sqrt{6}\)
C) π : \(\sqrt{6}\)
D) none
Answer:
B) \(\sqrt{\pi}\) : \(\sqrt{6}\)

Question 72.
In a hemisphere, r = 7 cm then CSA = ………………… cm².
A) 210
B) 308
C) 114
D) 112
Answer:
B) 308

Question 73.
In a cylinder, r = 7 cm then CSA = ………………. cm².
A) 1170
B) 1120
C) 2310
D) 1320
Answer:
C) 2310

Question 74.
Heap of stones is an example of ………………..
A) cylinder
B) cone
C) circle
D) none
Answer:
B) cone

Question 75.
In the figure, l² = ………………

A) h² + r²
B) \(\sqrt{l^2+h^2}\)
C) h² + r
D) h + r²
Answer:
A) h² + r²

Question 76.
Area of equilateral triangle of side ‘a’ units is …………….. sq. units.
A) \(\frac{1}{\sqrt{3}}\) a²
B) \(\frac{4}{\sqrt{3}}\) a²
C) \(\frac{\sqrt{3}}{4}\) a
D) \(\frac{\sqrt{3}}{4}\) a²
Answer:
D) \(\frac{\sqrt{3}}{4}\) a²

Question 77.
Perimeter of square is 20 cm then A = ………….. cm².
A) 12
B) 16
C) 25
D) none
Answer:
C) 25

Question 78.
Diagonal of rectangle is …………… units.
A) \(\sqrt{l^2+b^2}\)
B) \(\sqrt{l+b}\)
C) l + \(\sqrt{b}\)
D) \(\sqrt{l}\) + b
Answer:
A) \(\sqrt{l^2+b^2}\)

Question 79.
Volume of hollow cylinder is …………………
A) πR – r
B) πr² – R
C) πR² – r
D) π(R² – r²)
Answer:
D) π(R² – r²)

Question 80.
……………… gave the symbol π.
A) Euler
B) Pepe
C) Mount
D) None
Answer:
A) Euler

Question 81.
In a cone, (l + r) (l – r) = …………..
A) h²
B) 2h
C) h
D) none
Answer:
A) h²

Question 82.
A cuboid has dimensions 10x8x6 cm then its volume is ……………… cm³.
A) 190
B) 780
C) 680
D) 480
Answer:
D) 480

Question 83.
C.S.A of a cone is 4070 cm² and its diameter is 70 cm then slant height is ………………. cm
A) 27
B) 17
C) 37
D) 16
Answer:
C) 37

Question 84.
The sphere is of radius 2.1 cm then its volume is ………………. cm².
A) 38.08
B) 381.2
C) 83.01
D) none
Answer:
A) 38.08

Question 85.
In l² = h² + r², h = 15, r = 8 then l = ………….
A) 20
B) 17
C) 16
D) 19
Answer:
B) 17

Question 86.
The surface area of a sphere is 616 sq.cm. then its radius is ……………… cm.
A) 16
B) 12
C) 9
D) 7
Answer:
D) 7

Question 87.
In a cone, d = 14 cm, l = 10 cm then CSA = ………………….. cm².
A) 220
B) 140
C) 160
D) none
Answer:
A) 220

Question 88.
In a cube, a = 4 cm then TSA = ……………… cm².
A) 12
B) 70
C) 90
D) none
Answer:
C) 90

Question 89.
Number of edges of a cuboid is ………………
A) 11
B) 16
C) 10
D) 12
Answer:
D) 12

Question 90.
If the diagonals of a rhombus are 10 cm and 24 cm then area is ……………….. cm²
A) 110
B) 814
C) 413
D) 314
Answer:
A) 110

Question 91.
Volume of cone with d as diameter and h as height is …………………. units³.
A) \(\frac{\pi \mathrm{d}^2}{6}\)
B) \(\frac{\pi \mathrm{d}^2 \mathrm{~h}}{12}\)
C) \(\frac{\pi \mathrm{dh}^2}{12}\)
D) none
Answer:
B) \(\frac{\pi \mathrm{d}^2 \mathrm{~h}}{12}\)

Question 92.
The area of the base of a right circular cone is 78.5 cm². If its height is 12 cm then its volume is …………….. cm³.
A) 110
B) 814
C) 413
D) 314
Answer:
D) 314

Question 93.
The volume of a cuboid is 3,36,000 cm³. If; its area is 5,600 cm² then h = ……………… cm
A) 70
B) 60
C) 95.5
D) none
Answer:
B) 60

Question 94.
The volume of cone is 462 cm³, r = 7 cm then h = ……………….. cm.
A) 9
B) 10
C)11
D) none
Answer:
A) 9

Question 95.
The area of equilateral triangle is 36\(\sqrt{3}\) cm² then the perimeter is ……………. cm.
A) 36
B) 63
C) 16
D)10
Answer:
A) 36

Question 96.
Surface area of a cube of side 27 cm is ………………. cm³.
A) 1474
B) 8174
C) 1374
D) 4374
Answer:
D) 4374

Question 97.
The perimeter of an equilateral triangle is 60 cm then its area is ………………….. cm².
A) 149.3
B) 170.1
C) 137.4
D) 173.2
Answer:
D) 173.2

Question 98.
If the diagonal of a cube is 2.5 m then volume is ……………….. m³.
A) 3.01
B) 4.01
C) 8.1
D) none
Answer:
A) 3.01

Question 99.
r² = 1728 then r = ………………..
A) 13
B) 19
C) 10
D) 12
Answer:
D) 12

Question 100.
Number of faces of a cuboid is ………………..
A) 9
B) 10
C) 6
D) 8
Answer:
C) 6