Maths MCQ Class X Ch-12 | Surface Area & Volume

       Mathematics MCQ | Class 10 | Chapter 12

Surface Area & Volume

MCQ BASED ON CUBE AND CUBOID

Cube and cuboid have following properties

Both have 6 faces, 8 vertices and 12 edges.

Faces of cube are squares and faces of cube are rectangles.

Q1) The formula to find the surface area of a cuboid of length (l), breadth (b) and height (h) is:
a) lb + bh + hl
b) 2(lb + bh + hl)
c) 2(lbh)
d) lbh/2

Answer: b

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Q2) If the perimeter of one of the faces of a cube is 40 cm, then its volume is:
a) 6000 cm³
b) 1600 cm³
c) 1000 cm³
d) 600 cm³

Answer: c

Q3) The surface area of a cube whose edge equals to 3cm is:
a) 62 sq.cm
b) 30 sq.cm
c) 54 sq.cm
d) 90 sq.cm

Answer: c

Q4) The surface area of cuboid-shaped box having length = 80 cm, breadth = 40cm and height = 20cm is:

a) 11200 sq.cm
b) 13000 sq.cm
c) 13400 sq.cm
d) 12000 sq.cm

Answer: a

Hint: surface area of the box = 2(lb + bh + hl)
S.A. = 2[(80 × 40) + (40 × 20) + (20 × 80)]

Q5) The length of the longest pole that can be put in a room of dimension (10 m × 10 m × 5 m) is

a) 15 m
b) 16 m
c) 10 m
d) 12 m

Answer: a

Q6) The total surface area of a cube is 96 cm². The volume of the cube is:
a) 8 cm³
b) 512 cm³
c) 64 cm³
d) 27 cm³

Answer: c

Explanation:
We know that the TSA of the cone = 6a².
6a² = 96 cm²
a² = 96/6 = 16
a = 4 cm
The volume of cone = a³ cubic units
V = 43 = 64cm³.

Q7) The lateral surface area of a cube is 256 m². The volume of the cube is
a) 512 m³
b) 64 m³
c) 216 m³
d) 256 m³

Answer: a

Q8) The length of the longest pole that can be put in a room of dimensions (10 m × 10 m × 5m) is
a) 15m
b) 16m
c) 10m
d) 12m

Answer: a

Hint: Given: l = 10m, b = 10m, h = 5m
The length of the longest pole

= √[10² + 10² + 5²]

Q9) The number of planks of dimensions (4 m × 50 cm × 20 cm) that can be stored in a pit that is 16 m long, 12m wide and 4 m deep is
a) 1900
b) 1920
c) 1800
d) 1840

Answer: b

Explanation:
Volume of Plank = 400 cm × 50cm × 20cm
Volume of pits = 1600cm × 1200cm × 400cm
Number of planks = Volume of pits/Volume of planks
Hence, the number of pits = 1920

Q10) The total surface area of a cube is 96 cm². The volume of the cube is
a) 8 cm³

b) 512 cm³
c) 64 cm³
d) 27 cm³

Answer: c

Q11) The lateral surface area of a cube is 256 m². The volume of the cube is
a) 512 m³
b) 64 m³
c) 216 m³
d) 256 m³

Answer: a

Hint: The lateral surface area of cube = 4a²
4a² = 256
a² = 256/4 =64
a = 8 m
Hence, the volume of cube = a³ cube units
V = 8³ = 512 m³.

MCQ BASED ON RIGHT CIRCULAR CYLLINDER

Cylinder is a solid figure which have three faces, two faces at the top and bottom are plan surface and one is curved surface or Lateral surface.

Q12) If the radius of a cylinder is 4cm and height is 10cm, then the total surface area of a cylinder is:
a) 440 sq.cm
b) 352 sq.cm.
c) 400 sq.cm
d) 412 sq.cm

Answer: b

Hint: Total Surface Area of a Cylinder = 2πr(r + h)

Q13) The radius of a cylinder is doubled and the height remains the same. The ratio between the volumes of the new cylinder and the original cylinder is
a) 1 : 2
b) 3 : 1
c) 4 : 1
d) 1 : 8

Answer: c

Q14) In a cylinder, the radius is doubled and height is halved, the curved surface area will be

a) Halved
b) Doubled
c) Same
d) Four times

Answer: c

Hint: We know that the curved surface area of a cylinder is 2πrh
Given that, r = 2R, h = H/2
Hence, the CSA of new cylinder = 2π(2R)(H/2) = 2πRH
Therefore, the answer is “Same”.

Q15) The curved surface area of a right circular cylinder of height 14 cm is 88 cm². The diameter of the base is:
a) 2 cm
b) 3cm
c) 4cm
d) 6cm

Answer: a

Hint: Curved surface area of cylinder = 88 sq.cm
Height = 14 cm
2πrh = 88
r = 88/2πh
r =1 cm
Diameter = 2r = 2cm

Q16) Volume of hollow cylinder is
a) π(R² – r²)h
b) πR²h
c) πr²h
d) πr²(h1 – h1)

Answer: a

Q17) The Curved surface area of a right circular cylinder is 4.4 sq.cm. The radius of the base is 0.7 cm. The height of the cylinder will be:
a) 2 cm
b) 3 cm
c) 1 cm
d) 1.5 cm

Answer: c

Hint: Curved surface area of cylinder = 2πrh
2πrh = 4.4
h = 4.4/(2π x 0.7)
h = 1 cm

Q 18) The radii of two cylinders are in the ratio of 2 : 3 and their heights are in the ratio of 5 : 3. The ratio of their volumes is:
a) 10 : 17
b) 20 : 27
c) 17 : 27
d) 20 : 37

Answer: b

Hint:
Given that, the radii of two cylinders are in the ratio of 2 : 3
Hence, r₁ = 2r, r₂ = 3r
Also, given that, the height of two cylinders are in the ratio 5 : 3.
Hence, h₁ = 5h, h₂ = 3h
The ratio of the volume of two cylinders = V₁/V₂
= πr₁²h₁/πr₂²h₂
= [(2r)²(5h)]/[(3r)²(3h)]
Ratio of their volumes = (20r²h)/(27r²h) = 20/27 = 20 : 27.

Q 19) If the radius of a cylinder is 4cm and height is 10cm, then total surface area of cylinder is:
a) 440 sq.cm
b) 352 sq.cm.
c) 400 sq.cm
d) 412 sq.cm

Answer: b

MCQ BASED ON RIGHT CIRCULAR CONE

Cone is a solid figure which has two faces one is plane surface at the bottom and another is a curved surface.

Q 20) The diameter of the base of a cone is 10.5 cm, and its slant height is 10 cm. The curved surface area is:
a) 150 sq.cm
b) 165 sq.cm
c) 177 sq.cm
d) 180 sq.cm

Answer: b

Hint: Diameter = 10.5, Radius = 10.5/2
Slant height, l = 10cm
Curved surface area of cone = πrl = π(5.25)(10)
CSA = 165 sq.cm

Q 21) A cone is 8.4 cm high and the radius of its base is 2.1 cm. It is melted and recast into a shape. The radius of the sphere is
a) 4.2 cm
b) 2.1 cm
c) 2.4 cm
d) 1.6 cm

Answer b

Q 22) If slant height of the cone is 21cm and the diameter of the base is 24 cm. The total surface area of a cone is:
a) 1200.77 sq.cm
b) 1177 sq.cm
c) 1222.77 sq.cm
d) 1244.57 sq.cm

Answer: d

Hint: Total surface area = πr(l + r)

Q 23) A cone is 8.4 cm high and the radius of its base is 2.1 cm. It is melted and recast into a sphere. The radius of the sphere is
a) 4.2 cm
b) 2.1 cm
c) 2. 4 cm
d) 1.6 cm

Answer: b

Hint:  Given that the height of cone = 8.4 cm
Radius of cone = 2.1 cm
Also, given that the volume of cone = volume of a sphere
(1/3)πr²h = (4/3)πr³
(1/3)π(2.1)²(8.4) = (4/3)πr³

Q24) Diameter of the base of a cone is 10.5 cm and its slant height is 10 cm. The curved surface area is:
a) 150 sq.cm
b) 165 sq.cm
c) 177 sq.cm
d) 180 sq.cm

Answer: b

Q25) The total surface area of a cone whose radius is r/2 and slant height 2l is
a) 2πr(l + r)
b) πr(l + (r/4))
c) πr(l + r)
d) 2πrl

Answer: b

Hint: The total surface area of cone = πr(l + r) square units.

MCQ BASED ON SPHERE AND HEMI-SPHERE

Sphere is solid figure which has only one curved surface.
Hemi sphere is a solid figure which has two faces, one is plane surface at the top and another is curved surface.

Q26) The volume of a hemisphere whose radius is r is:
a) 4/3 πr³
b) 4πr³
c) 2πr³
d) 2/3 π r³

Answer: d

Q27) The surface area of a sphere of radius 14 cm is:
a) 1386 sq.cm
b) 1400 sq.cm
c) 2464 sq.cm
d) 2000 sq.cm

Answer: c

Hint: Surface area = 4πr²
= 4 x 22/7 x (14)² = 2464 sq.cm.

Q 28)The radius of a hemispherical balloon increases from 6 cm to 12 cm as air is being pumped into it. The ratios of the surface areas of the balloon in the two cases is
a) 1 : 4
b) 1 : 3
c) 2 : 3
d) 2 : 1

Answer: a

Q29) The radius of a sphere is 2r, then its volume will be
a) (4/3) πr³
b) 4πr³
c) (8/3) πr³
d) (32/3) πr³

Answer: d

Q 30) The radius of a hemispherical balloon increases from 6 cm to 12 cm as air is being pumped into it. The ratio of the surface areas of the balloon in the two cases is
a) 1 : 4
b) 1 : 3
c) 2 : 3
d) 2 : 1

Answer: a

Hint: We know that the total surface area of the hemisphere = 3πr² square units.
If r= 6cm, then TSA = 3π(6)²
If r = 12 cm, then TSA = 3π(12)²
Then the ratio = 3π(6)² / 3π(12)²
Ratio = 1/4, which is equal to 1:4.

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