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All questions of Surface Area & Volumes for Class 9 Exam

A rectangular sand box is 5 m wide and 2 m long. How many cubic metres of sand are needed to fill the box upto a depth of 10 cm ?
  • a)
    1
  • b)
    10
  • c)
    100
  • d)
    1000
Correct answer is option 'A'. Can you explain this answer?

Arizona Academy answered
To calculate the volume of sand needed to fill the rectangular sandbox, we can use the formula:Volume = Length × Width × DepthGiven:
Length = 2 m
Width = 5 m
Depth = 10 cm = 0.1 mSubstituting the values into the formula:Volume = 2 m × 5 m × 0.1 m
Volume = 1 cubic meterTherefore, the correct answer is A: 1 cubic meter.
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A beam 9 m long, 40 cm wide and 20 cm deep is made up of iron which weighs 50 kg per cubic metre.
The weight of the beam is :
  • a)
    27 kg
  • b)
    36 kg
  • c)
    48 kg 
  • d)
    56 kg
Correct answer is option 'B'. Can you explain this answer?

Arizona Academy answered
To find the weight of the iron beam, we need to calculate its volume and then multiply it by the weight of 1 cubic meter of iron, which is given as 50 kg.Given:
Length of beam (l) = 9 m
Breadth (b) = 40 cm = 0.4 m
Height (h) = 20 cm = 0.2 m
Weight of 1 cubic meter of iron = 50 kgVolume of the beam = l × b × h = 9 m × 0.4 m × 0.2 m = 0.72 cubic metersWeight of the beam = Volume × Weight of 1 cubic meter of iron = 0.72 cubic meters × 50 kg/cubic meter = 36 kg
Therefore, the weight of the iron beam is 36 kg, which corresponds to option B.

A conical tomb of base diameter 24m and height 16 m. What is the curved surface area?
  • a)
    200π sq m
  • b)
    240π sq m
  • c)
    300π sq m
  • d)
    64π sq m
Correct answer is option 'B'. Can you explain this answer?

Sagnik Menon answered
The formula for the curved surface area of a cone is πrs, where r is the radius of the base and s is the slant height. To find the slant height, we can use the Pythagorean theorem: s² = r² + h², where h is the height of the cone.

In this case, the radius is half of the base diameter, so r = 12m. Using the Pythagorean theorem, we get:

s² = 12² + 16²
s² = 144 + 256
s² = 400
s = 20m

Now we can calculate the curved surface area:

A = πrs
A = π(12)(20)
A = 240π

Using a calculator, we can approximate this to:

A ≈ 753.98

Therefore, the curved surface area of the conical tomb is approximately 753.98 square meters.

The maximum length of a pencil that can be kept in a rectangular box of dimensions 8 cm × 6 cm × 2 cm, is:
  • a)
    2√13 cm
  • b)
    2√14 cm
  • c)
    2√26 cm
  • d)
    10√2 cm
Correct answer is option 'C'. Can you explain this answer?

Arizona Academy answered
To find the maximum length of a pencil that can be kept in a rectangular box of dimensions 8 cm × 6 cm × 2 cm, we need to find the length of the diagonal of the box, which will be the maximum length of the pencil that can fit inside the box.Using the Pythagorean theorem, the length of the diagonal of the box can be found as:Diagonal = √(length² + breadth² + height²)
Diagonal = √(8² + 6² + 2²)
Diagonal = √(64 + 36 + 4)
Diagonal = √104
Diagonal = 2√26Therefore, the maximum length of a pencil that can be kept in the rectangular box is 2√26 cm, which corresponds to option C.

The surface area of a cube of side 27 cm is :
  • a)
    2916 cm2
  • b)
    729 cm2
  • c)
    4374 cm2
  • d)
    19683 cm2
Correct answer is option 'C'. Can you explain this answer?

Arizona Academy answered
The surface area of a cube of side 27 cm can be found using the formula:Surface area of a cube = 6a^2, where a is the length of the side of the cube.Given:
Length of side of the cube = 27 cmSubstituting the value into the formula:Surface area of the cube = 6 × 27^2
Surface area of the cube = 6 × 729
Surface area of the cube = 4374 cm^2Therefore, the surface area of the cube of side 27 cm is 4374 cm^2, which corresponds to option C

The total surface area of a cube is 96 cm2 . The volume of the cube is
  • a)
    64 cm3
  • b)
    27 cm3
  • c)
    512 cm3
  • d)
    9 cm3
Correct answer is option 'A'. Can you explain this answer?

Ananya Das answered
Surface area of a cube = 96 cm2
Surface area of a cube = 6 (Side)2 = 96 ⇒  (Side)2 = 16
⇒ (Side) = 4 cm
[taking positive square root because side is always a positive quantity]
Volume of cube = (Side)3 = (4)3 = 64 cm3
Hence, the volume of the cube is 64 cm3.

The radius of two similar right circular cones are 2 cm and 6 cm. The ratio of their volumes is
  • a)
    1 : 3
  • b)
    1 : 9
  • c)
    9 : 1
  • d)
    1 : 27
Correct answer is option 'D'. Can you explain this answer?

Nilanjan Sharma answered
Let the volume two cones be v1 & v2 & r1 and r2 be the radii of the two right circular cones & height of the two cones be h.

Ratio of base radii = r1:r2= 3 : 5

Volume of cone = 1/3πr^2h

Volume of first cone (v1)1/Volume of second cone (v2)

=(1/3�π�r1^2�h)/(1/3�π�r2^2�h)

= (1/3�π�3^2�h)/(1/3�π�5^2�h)

= r1^2/r2^2

= 3^2/5^2

= 9/25

= 9 : 25
Hence, the ratio of their volumes is 9 : 25

The cost of cementing the inner curved surface of a 14 m deep well of radius 2 m at the rate of Rs 2 per m2 is
  • a)
    Rs 352.
  • b)
    Rs 176.
  • c)
    Rs 56.
  • d)
    Rs 112.
Correct answer is option 'A'. Can you explain this answer?

Kamna Science Academy answered
Depth of well(h) = 14m
radius of well(r) = 2m
Inner surface area of well(like a cylinder) = 2πrh 
surface area= 2 x 22/7 x 2 x 14 = 176 m2
cost of cementing = ₹2 per m2
Total Cost = 176 x 2 = ₹352

The diameter of a sphere whose volume is 1047.816 cm3 is​
  • a)
    8.6 cm
  • b)
    10.6 cm
  • c)
    16.6 cm
  • d)
    12.6 cm
Correct answer is option 'D'. Can you explain this answer?

Abhay Chawla answered
Given: Volume of the sphere = 1047.816 cm³

To find: Diameter of the sphere

Formula used: Volume of sphere = (4/3)πr³, where r is the radius of the sphere

Explanation:

We know that the volume of the sphere is given by the formula (4/3)πr³, where r is the radius of the sphere.

We can find the radius of the sphere by using the formula:

r = (3V/4π)^(1/3), where V is the volume of the sphere.

Substituting the given value of V, we get:

r = (3 x 1047.816/4π)^(1/3)

r = 6.3 cm (approx.)

Now, we can find the diameter of the sphere by multiplying the radius by 2.

Diameter = 2 x radius

Diameter = 2 x 6.3

Diameter = 12.6 cm

Therefore, the diameter of the sphere is 12.6 cm, which is option D.

The total surface area of a hemispherical bowl of diameter 28 cm is​
  • a)
    1848 cm2
  • b)
    1800 cm2
  • c)
    1600 cm2
  • d)
    1648 cm2
Correct answer is option 'A'. Can you explain this answer?

Sarita Reddy answered
Correct, option 'A' is the correct answer.
The total surface area of a hemispherical bowl can be calculated by using the formula 4πr^2, where r is the radius of the bowl.
Given the diameter of the bowl is 28 cm, the radius of the bowl is 14cm.
So, the total surface area of the hemispherical bowl of diameter 28 cm is 4π(14)^2 = 4π*196 =784π = 1848 cm^2 (approximately)
Alternatively, we can also use the formula 2πr^2 + 2πrr (r being the radius of the bowl) to calculate the total surface area of the hemispherical bowl.
In this case, 2π(14)^2 + 2π(14) 14 = 2π196 + 2π196 = 392π = 1848 cm^2 (approximately)
Hence the answer is A. 1848 cm2

The surface area of a sphere of radius 7 cm is​
  • a)
    636 cm2
  • b)
    616 cm2
  • c)
    702 cm2
  • d)
    546 cm2
Correct answer is option 'B'. Can you explain this answer?

Kumar Aryan answered
As we know that the formula of surface area of a sphere is 4πr
here the given radius is 7cm
so by using formula of surface area of sphere we find that
=> 4×7×7×22÷7 = 616 cm²
which is option (b).

The volume of a cube with surface area 384 sq. cm, is :
  • a)
    216 cm3
  • b)
    256 cm3
  • c)
    484 cm3
  • d)
    512 cm3
Correct answer is option 'D'. Can you explain this answer?

Sanjana Bose answered
The surface area of a cube is given by 6 times the area of one face, and the area of a face of a cube is equal to the length of one edge squared. So if the surface area of the cube is 384 cm^2, we can write the equation:
6 * edge^2 = 384
Solving for the edge length:
edge^2 = 64
edge = 8
The volume of a cube is equal to the length of one edge cubed, so the volume of this cube is:
volume = 8^3 = 512 cm^3

A sphere has a surface area of 301.84 cm2. Its diameter is​
  • a)
    8.4 cm
  • b)
    7.4 cm
  • c)
    9.8 cm
  • d)
    10.6 cm
Correct answer is option 'C'. Can you explain this answer?

Bishwanath Patra answered
Surface area of sphere= 301.84 cm^2, 4 × 22/7 ×r^2 =301.84 , r^2 = 301.84 ×7 / 22, r^2 = 24.01 r = 4.9cm , diameter = 2r =2×4.9 =9.8cm

If the ratio of volumes of two spheres is 1 : 8, then the ratio of their surface areas is :
  • a)
    1 : 2
  • b)
    1 : 4
  • c)
    1 : 8
  • d)
    1 : 16
Correct answer is option 'B'. Can you explain this answer?

Sarita Reddy answered
The correct answer is option 'B', the ratio of surface areas is 1:4.
The ratio of the surface areas of two spheres is the square of the ratio of their radii. If the ratio of volumes of two spheres is 1:8, then the ratio of their radii is 3:2 . Therefore, the ratio of the surface areas of the two spheres is (3/2)^2 = 9/4 = 1:4

If a hemi-spherical dome has an inner diameter of 28 m, then its volume (in m3) is :
  • a)
    6186.60
  • b)
    5749.33
  • c)
    7099.33
  • d)
    7459.33
Correct answer is option 'B'. Can you explain this answer?

Tia Shah answered
Given information:

- Inner diameter of the hemi-spherical dome = 28 m

Formula:

- The formula to calculate the volume of a hemisphere is V = (2/3)πr³, where V is the volume and r is the radius of the hemisphere.

Calculation:

- The radius of the hemisphere can be calculated by dividing the inner diameter by 2.
- Inner radius = 28 m / 2 = 14 m

Substitute the values:

- V = (2/3)π(14)³
- V = (2/3) × 3.14 × 14³
- V = (2/3) × 3.14 × 2744
- V = 1813.76 m³ (approx)

Answer:

The volume of the hemi-spherical dome is approximately 1813.76 m³, which is closest to option 'B' (5749.33 m³).

The volume of a sphere is 38808 cu.cm. The curved surface area of the sphere (in cm2) is :
  • a)
    5544
  • b)
    1386
  • c)
    8316
  • d)
    4158
Correct answer is option 'A'. Can you explain this answer?

Advait Iyer answered
To find the curved surface area of a sphere, we need to know the volume of the sphere. Let's calculate the radius of the sphere first using the given volume.

Let the radius of the sphere be 'r'.

The formula for the volume of a sphere is given by:

V = (4/3)πr^3

Given that the volume of the sphere is 38808 cu.cm, we can substitute this value into the formula:

38808 = (4/3)πr^3

To find the value of 'r', we can rearrange the equation:

r^3 = (3/4)(38808/π)

r^3 = 29106

Taking the cube root of both sides, we find:

r ≈ 30

Now that we know the radius of the sphere is approximately 30 cm, we can calculate the curved surface area.

The formula for the curved surface area of a sphere is given by:

CSA = 4πr^2

Substituting the value of 'r' into the formula:

CSA = 4π(30)^2

CSA ≈ 4π(900)

CSA ≈ 3600π

Since the value of π is approximately 3.14, we can approximate the curved surface area:

CSA ≈ 3600(3.14)

CSA ≈ 11304

Therefore, the curved surface area of the sphere is approximately 11304 sq.cm.

None of the given options match the calculated value of the curved surface area. It is possible that there is an error in the question or options provided.

The volume of a spherical shell whose internal and external diameters are 8 cm and 10 cm respectively (in cubic cm) is:
  • a)
    122π/3
  • b)
    244π/3
  • c)
    212
  • d)
    257
Correct answer is option 'B'. Can you explain this answer?

Sarita Reddy answered
The volume of a spherical shell is the difference between the volumes of the two spheres that make up the shell. The internal sphere has a diameter of 8 cm, and the external sphere has a diameter of 10 cm. To find the volume of the spherical shell, we can first find the volume of each of the two spheres and then subtract the volume of the smaller sphere from the volume of the larger sphere.
The volume of a sphere is given by the formula V = (4/3)πr^3, where V is the volume, r is the radius of the sphere, and π is a mathematical constant approximately equal to 3.14159. The radius of the internal sphere is 4 cm (half of the diameter), and the radius of the external sphere is 5 cm (half of the diameter). Therefore, the volume of the internal sphere is (4/3)π(4^3) = (4/3)π64 = 256π/3 cubic cm, and the volume of the external sphere is (4/3)π(5^3) = (4/3)π125 = 500π/3 cubic cm.
To find the volume of the spherical shell, we subtract the volume of the internal sphere from the volume of the external sphere: 500π/3 - 256π/3 = 244π/3 cubic cm. Therefore, the volume of the spherical shell is 244π/3 cubic cm, which corresponds to answer choice (b).

Given that 1 cm3 of a metal weighs 5 gms, the weight of a cylindrical metal container with base radius 10.5 cm and height 60 cm, is :
  • a)
    97.65 kg
  • b)
    48.75 kg
  • c)
    103.95 kg
  • d)
    102.45 kg
Correct answer is option 'C'. Can you explain this answer?

Arizona Academy answered
Given:
Radius = 10.5 cm
Height = 6 m
Weight of 1 cm3 = 5 grams
Formula used:
Volume of cylinder = πr2h
1 m = 100 cm
⇒ 6 m = 600 cm
1 kg = 1000 gram
Calculation:
According to the question
Volume of cylinder = πr2h
⇒ (3.14 × 10.5 × 10.5 × 600) cm3
⇒ 207711 cm3
Now, Weight of 1 cm3​ = 5 grams
So, Weight of 207,711 cm3 = 5 × 207711
⇒ 1,038,555 grams
⇒ 1038.555 kg ~ 1038.5 kg

The length of the longest rod that can fit in a cubical vessel of side 10 cm, is
  • a)
    10 cm
  • b)
    10√2 cm
  • c)
    10√3 cm
  • d)
    20 cm
Correct answer is option 'C'. Can you explain this answer?

Bably Bhatt answered
The longest stick that can be fit is the length of the diagonal of the cubical vessel.

Therefore, length of diagonal =(10)2+(10)2+(10)2​ =3(10)2​=103​cm

A hemispherical bowl is made of steel 0.25 cm thick. If the inner radius of the bowl is 3.25 cm, then the outer curved surface area of the bowl is
  • a)
    154 cm2.
  • b)
    77 cm2.
  • c)
    115.5 cm2.
  • d)
    38.5 cm2.
Correct answer is option 'B'. Can you explain this answer?

Aditi Bhosale answered
Given- Inner radius-3.25cm, thickness- 0.25cm
So, outer radius=inner radius+thickness
=3.25+0.25=3.5 cm.
Now, outer curved surface area of hemispherical bowl=2πr²
=2×22/7×3.5×3.5
=44×1.75
=77cm², so option 'B' is correct

Chapter doubts & questions for Surface Area & Volumes - Mathematics (Maths) Class 9 2025 is part of Class 9 exam preparation. The chapters have been prepared according to the Class 9 exam syllabus. The Chapter doubts & questions, notes, tests & MCQs are made for Class 9 2025 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests here.

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