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Surface Areas and Volumes: 2 marks Questions (CBSE Class 10)

22 different 2 marks questions on Surface Areas and Volumes from CBSE Class 10 Maths board exams 2022–2026, newest first.

1 mark (54)2 marks (22)3 marks (17)4 marks (27)5 marks (41)

Q252 marksVery Short AnswerSurface Areas and Volumes CBSE 2026 · Standard 30/3/1

A toy is in the form of a cone mounted on a hemisphere of radius 7 cm. The total height of the toy is 31 cm. Find the total surface area of the toy.

Diagram for CBSE 2026 Class 10 Maths question 25

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Answer: 858 cm

^{2}

Height of cone $= 31 - 7 = 24$ cm, radius $= 7$ cm
Slant height $l = 2 4^{2} + 7^{2} = 625 = 25$ cm
TSA = CSA of cone + CSA of hemisphere $= π r l + 2 π r^{2}$
$= \frac{22}{7} \times 7 \times 25 + 2 \times \frac{22}{7} \times 7 \times 7 = 550 + 308 = 858$ cm $^{2}$

Also asked in: 2026 Standard 30/3/3

Q252 marksVery Short AnswerSurface Areas and Volumes CBSE 2026 · Standard 30/3/2

1000 small thermocol balls of radius 0.5 cm are kept in a spherical balloon of radius 20 cm. Find the volume of air in the balloon.

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Answer: 33000 cm

^{3}

Volume of air = volume of balloon − volume of 1000 balls
$= \frac{4}{3} π (2 0^{3} - 1000 \times 0. 5^{3}) = \frac{4}{3} \times \frac{22}{7} \times (8000 - 125)$
$= \frac{4}{3} \times \frac{22}{7} \times 7875 = 33000$ cm $^{3}$

Q22 marksVery Short AnswerSurface Areas and Volumes CBSE 2022 · Basic 430/1/1Not in current syllabus

A solid metallic sphere of radius 3 cm is melted and recast into the shape of a solid cylinder of radius 2 cm. Find the height of the cylinder.

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Answer: 9 cm

Volume of sphere $= \frac{4}{3} π (3)^{3} = 36 π$ cm $^{3}$
Volume of cylinder $= π (2)^{2} h = 4 π h$
Volumes are equal: $4 π h = 36 π$
$h = 9$ cm

Also asked in: 2022 Basic 430/1/2

Q52 marksVery Short AnswerSurface Areas and Volumes CBSE 2022 · Basic 430/1/3Not in current syllabus

A solid hemisphere of radius 8 cm is melted and recast into 4 identical right circular solid cones of base radius 4 cm. Find the height of the cone.

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Answer: 16 cm

Volume of hemisphere $= \frac{2}{3} π (8)^{3} = \frac{1024 π}{3}$ cm $^{3}$
Volume of 4 cones $= 4 \times \frac{1}{3} π (4)^{2} h = \frac{64 π h}{3}$
$\frac{64 π h}{3} = \frac{1024 π}{3}$
$h = 16$ cm

Q32 marksVery Short AnswerSurface Areas and Volumes CBSE 2022 · Basic 430/2/1

3 cubes each of 8 cm edge are joined end to end. Find the total surface area of the cuboid so formed.

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Answer: 896 cm²

Cuboid formed: $l = 3 \times 8 = 24$ cm, $b = 8$ cm, $h = 8$ cm.
TSA $= 2 (l b + bh + h l) = 2 (24 \times 8 + 8 \times 8 + 8 \times 24)$
$= 2 (192 + 64 + 192) = 2 \times 448 = 896$ cm².

Q62 marksVery Short AnswerSurface Areas and Volumes CBSE 2022 · Basic 430/2/2

3 cubes each of 8 cm edge are joined end to end. Find the total surface area of the cuboid.

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Answer: 896 cm²

Cuboid formed: $l = 3 \times 8 = 24$ cm, $b = 8$ cm, $h = 8$ cm.
TSA $= 2 (l b + bh + h l) = 2 (24 \times 8 + 8 \times 8 + 8 \times 24)$
$= 2 (192 + 64 + 192) = 2 \times 448 = 896$ cm².

Q32 marksVery Short AnswerSurface Areas and Volumes CBSE 2022 · Basic 430/2/3

A metallic hollow cylindrical pipe has outer and inner radii as 6 cm and 4 cm respectively. Find the volume of the metal used in the pipe of length of 14 cm.

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Answer: 880 cm³

Volume of metal $= π (R^{2} - r^{2}) h = \frac{22}{7} \times (36 - 16) \times 14$
$= 22 \times 20 \times 2 = 880$ cm³.

Q42 marksVery Short AnswerSurface Areas and Volumes CBSE 2022 · Basic 430/3/1

A cubical block of side 7 cm is surmounted by a hemisphere of largest possible diameter as shown in Figure 1. Find the total surface area of the solid.

Diagram for CBSE 2022 Class 10 Maths question 4

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Answer: 332.5 cm

^{2}

Largest hemisphere has diameter 7 cm, so $r = 3.5$ cm.
TSA = surface area of cube − area of base circle of hemisphere + curved surface area of hemisphere
$= 6 (7)^{2} - π r^{2} + 2 π r^{2} = 294 + π r^{2}$
$= 294 + \frac{22}{7} \times 3.5 \times 3.5 = 294 + 38.5 = 332.5$ cm $^{2}$

Also asked in: 2022 Basic 430/3/2

Q4 (OR) (OR)2 marksVery Short AnswerSurface Areas and Volumes CBSE 2022 · Basic 430/3/1Not in current syllabus

How many solid cones of height 3 cm and radius 2 cm can be formed by melting a solid sphere of radius 3 cm ?

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Answer: 9 cones

Volume of sphere $= \frac{4}{3} π (3)^{3} = 36 π$ cm $^{3}$
Volume of one cone $= \frac{1}{3} π (2)^{2} (3) = 4 π$ cm $^{3}$
Number of cones $= \frac{36 π}{4 π} = 9$

Also asked in: 2022 Basic 430/3/2, 2022 Basic 430/3/3

Q62 marksVery Short AnswerSurface Areas and Volumes CBSE 2022 · Basic 430/3/3

A cubical block of side 7 cm is surmounted by a hemisphere of largest possible diameter as shown in Figure 2. Find the total surface area of the solid.

Diagram for CBSE 2022 Class 10 Maths question 6

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Answer: 332.5 cm

^{2}

Largest hemisphere has diameter 7 cm, so $r = 3.5$ cm.
TSA = surface area of cube − area of base circle of hemisphere + curved surface area of hemisphere
$= 6 (7)^{2} - π r^{2} + 2 π r^{2} = 294 + π r^{2}$
$= 294 + \frac{22}{7} \times 3.5 \times 3.5 = 294 + 38.5 = 332.5$ cm $^{2}$

Q62 marksVery Short AnswerSurface Areas and Volumes CBSE 2022 · Basic 430/4/1

Find the curved surface area of a right circular cone whose height is 15 cm and base radius is 8 cm. [Use $π = \frac{22}{7}$ ]

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Answer:

\frac{2992}{7} cm^{2} \approx 427.43 cm^{2}

Slant height $l = h^{2} + r^{2} = 225 + 64 = 289 = 17$ cm.
CSA $= π r l = \frac{22}{7} \times 8 \times 17 = \frac{2992}{7}$ .
CSA $= 427 \frac{3}{7} \approx 427.43 cm^{2}$ .

Also asked in: 2022 Basic 430/4/3

Q6 (OR) (OR)2 marksVery Short AnswerSurface Areas and Volumes CBSE 2022 · Basic 430/4/1

The surface area of a sphere is 616 sq cm. Find its radius. [Use $π = \frac{22}{7}$ ]

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Answer: 7 cm

$4 π r^{2} = 616$ .
$4 \times \frac{22}{7} \times r^{2} = 616 \Rightarrow r^{2} = \frac{616 \times 7}{88} = 49$ .
$r = 7$ cm.

Also asked in: 2022 Basic 430/4/3

Q42 marksVery Short AnswerSurface Areas and Volumes CBSE 2022 · Basic 430/4/2

A solid is in the shape of a cone standing on a hemisphere with both their radii being equal to 1 cm and the height of the cone is equal to its radius. Find the volume of the solid in terms of $π$ .

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Answer:

π cm^{3}

$r = h = 1$ cm.
Volume $= \frac{1}{3} π r^{2} h + \frac{2}{3} π r^{3} = \frac{1}{3} π + \frac{2}{3} π$ .
$= π cm^{3}$ .

Q4 (OR) (OR)2 marksVery Short AnswerSurface Areas and Volumes CBSE 2022 · Basic 430/4/2

Find the volume of a solid hemisphere whose total surface area is 462 sq.m.

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Answer:

\frac{2156}{3} m^{3} \approx 718.67 m^{3}

TSA of a solid hemisphere $= 3 π r^{2} = 462$ .
Taking $π = \frac{22}{7}$ : $r^{2} = \frac{462 \times 7}{66} = 49 \Rightarrow r = 7$ m.
Volume $= \frac{2}{3} π r^{3} = \frac{2}{3} \times \frac{22}{7} \times 343 = \frac{2156}{3} \approx 718.67 m^{3}$ .

Q22 marksVery Short AnswerSurface Areas and Volumes CBSE 2022 · Standard 30/1/1Not in current syllabus

A solid metallic sphere of radius 10.5 cm is melted and recast into a number of smaller cones, each of radius 3.5 cm and height 3 cm. Find the number of cones so formed.

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Answer: 126

Volume of sphere $= \frac{4}{3} π (10.5)^{3}$ .
Volume of one cone $= \frac{1}{3} π (3.5)^{2} (3)$ .
Number of cones $= \frac{\frac{4}{3} π ( 10.5 ) ^{3}}{\frac{1}{3} π ( 3.5 ) ^{2} \times 3} = \frac{4 \times 10.5 \times 10.5 \times 10.5}{3.5 \times 3.5 \times 3}$
$= \frac{4 \times 3 \times 3 \times 10.5}{3} = 126$

Also asked in: 2022 Standard 30/1/3

Q42 marksVery Short AnswerSurface Areas and Volumes CBSE 2022 · Standard 30/1/2Not in current syllabus

A cone of height 28 cm and radius of base 7 cm is made up of modelling clay. A child reshapes it in the form of a sphere. Find the radius of the sphere.

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Answer: 7 cm

Volume is unchanged: $\frac{4}{3} π R^{3} = \frac{1}{3} π (7)^{2} (28)$ .
$4 R^{3} = 49 \times 28 \Rightarrow R^{3} = 343$
$R = 7$ cm.

Q32 marksVery Short AnswerSurface Areas and Volumes CBSE 2022 · Standard 30/2/1Not in current syllabus

A solid piece of metal in the form of a cuboid of dimensions 11 cm $\times$ 7 cm $\times$ 7 cm is melted to form ‘n’ number of solid spheres of radii $\frac{7}{2}$ cm each. Find the value of n.

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Answer: n = 3

Volume of cuboid $= 11 \times 7 \times 7 = 539$ cm $^{3}$ .
Volume of one sphere $= \frac{4}{3} π r^{3} = \frac{4}{3} \times \frac{22}{7} \times \frac{7}{2} \times \frac{7}{2} \times \frac{7}{2} = \frac{539}{3}$ cm $^{3}$ .
n $\times \frac{539}{3} = 539$
n $= 3$ .

Also asked in: 2022 Standard 30/2/2, 2022 Standard 30/2/3

Q42 marksVery Short AnswerSurface Areas and Volumes CBSE 2022 · Standard 30/3/1Not in current syllabus

150 spherical marbles, each of diameter 1.4 cm, are dropped in a cylindrical vessel of diameter 7 cm containing some water, and are completely immersed in water. Find the rise in the level of water in the cylindrical vessel.

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Answer: 5.6 cm

Radius of each marble $= 0.7$ cm; volume of 150 marbles $= 150 \times \frac{4}{3} π (0.7)^{3} = 200 \times 0.343 π = 68.6 π$ cm $^{3}$ .
Radius of vessel $= 3.5$ cm. Let the water rise by h cm: $π (3.5)^{2} h = 12.25 π h$ .
$12.25 π h = 68.6 π \Rightarrow h = \frac{68.6}{12.25} = 5.6$ cm.

Also asked in: 2022 Standard 30/3/2, 2022 Standard 30/3/3

Q4 (OR) (OR)2 marksVery Short AnswerSurface Areas and Volumes CBSE 2022 · Standard 30/3/1

Three cubes of side 6 cm each, are joined as shown in Figure 1. Find the total surface area of the resulting cuboid.

Diagram for CBSE 2022 Class 10 Maths question 4 (OR)

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Answer: 504 cm

^{2}

Joining three cubes of side 6 cm end to end gives a cuboid of length $3 \times 6 = 18$ cm, breadth 6 cm and height 6 cm.
TSA $= 2 (l b + bh + h l) = 2 (18 \times 6 + 6 \times 6 + 6 \times 18)$
$= 2 (108 + 36 + 108) = 2 \times 252 = 504$ cm $^{2}$ .

Also asked in: 2022 Standard 30/3/2

Q6 (OR) (OR)2 marksVery Short AnswerSurface Areas and Volumes CBSE 2022 · Standard 30/3/3

Three cubes of side 6 cm each, are joined as shown in Figure 2. Find the total surface area of the resulting cuboid.

Diagram for CBSE 2022 Class 10 Maths question 6 (OR)

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Answer: 504 cm

^{2}

Joining three cubes of side 6 cm end to end gives a cuboid of length $3 \times 6 = 18$ cm, breadth 6 cm and height 6 cm.
TSA $= 2 (l b + bh + h l) = 2 (18 \times 6 + 6 \times 6 + 6 \times 18)$
$= 2 (108 + 36 + 108) = 2 \times 252 = 504$ cm $^{2}$ .

Q62 marksVery Short AnswerSurface Areas and Volumes CBSE 2022 · Standard 30/4/1

The curved surface area of a right circular cylinder is 176 sq cm and its volume is 1232 cu cm. What is the height of the cylinder ?

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Answer: 2 cm

$2 π r h = 176$ and $π r^{2} h = 1232$ .
Dividing: $\frac{π r ^{2} h}{2 π r h} = \frac{1232}{176} \Rightarrow \frac{r}{2} = 7 \Rightarrow r = 14$ cm
$2 \times \frac{22}{7} \times 14 \times h = 176 \Rightarrow 88 h = 176$
$h = 2$ cm

Also asked in: 2022 Standard 30/4/2, 2022 Standard 30/4/3

Q6 (OR) (OR)2 marksVery Short AnswerSurface Areas and Volumes CBSE 2022 · Standard 30/4/1

The largest sphere is carved out of a solid cube of side 21 cm. Find the volume of the sphere.

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Answer: 4851

cm^{3}

Diameter of the largest sphere = side of cube = 21 cm, so $r = 10.5$ cm.
Volume $= \frac{4}{3} π r^{3} = \frac{4}{3} \times \frac{22}{7} \times 10.5 \times 10.5 \times 10.5$
$= 4851$ $cm^{3}$

Also asked in: 2022 Standard 30/4/2, 2022 Standard 30/4/3

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