**Surface Area and Volume**

Surface Area and Volume are the main chapter in mathematics for class 9th and 10th. Cuboid, Cube, Cylinder, Cone, Sphere, Hemisphere are the main section under the **Surface Area and Volume** chapter. The questions are asked in the examination contain 12 marks. So in order to secure these marks you need to make command on volume and surface area formulas. Apart from it students can read the examples and its solution to get the idea of solving asked question in the examination. For the ease of the students of Class 9 & 10 we are sharing 20 important Surface Area and Volume Questions & Answers at below section of this page which is created by the team members of www.recruitmentinboxx.com

**Surface Area and Volume**

__Surface Area and Volume Formulas Chart__

Easy Tricks To Remember: __Cylinder Volume Formula__

__Volume And Surface Area Examples__:

**Example1:**

This pyramid is made up of four equilateral triangles.

Here we just need to find the area of one triangle and multiply it by four sides:

Area of 1 triangle = ½bh = ½(8 x 6.9) = 27.6 cm^{2}

Now, multiply that by four sides, and we’re done.

110.4 cm^{2}

**Example2:**

The area of the circular base is equal to:

(π)(5^^{2}) = 25 (π) cm^^{2} = 78.5 cm^^{2}

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**Example 3:**

This cylinder has two circles (each with a radius of 2 cm) and one rectangle (with a length of 5.8 cm and a width the circumference of the circles).

Circle 1

π x 2^{2} = 4π 12.56 cm^{2}

Circle 2 π x 2^{2} = 4π 12.56 cm^{2}

Rect 1 5.8 x 4π = 23.^{2}π

72.85 cm^{2}

Total 97.97 cm^{2}

__Surface Area and Volume Questions & Answers__

Q.1 The altitude of a circular cylinder is increased six times and the base area is decreased to one-ninth of its value. The factor by which the lateral surface of the cylinder increases is….

- ½ m
- 2/3 m
- 3/2 m
- 2 m

Ans. 4

Q.2 The radii of the bases of a cylinder and a cone are in the ratio 3: 4. If height of the cylinder and cone are in the ratio 2: 3, then their volumes are in the ratio….

- 9: 8
- 8: 9
- 3: 4
- 4: 3

Ans. 4

Q.3 If area of the diagonal section of a cube is equal to 4Ö2 cm², then edge of the cube is….

- 4 cm
- 3 cm
- 2Ö2 cm
- 2 cm

Ans. 4

Q.4 A hall is 15 m long and 12 m broad. If the sum of the areas of the floor and the ceiling is equal to the sum of the areas of four walls, the volume of the hall is:

- 720
- 900
- 1200
- 1800

Ans. 3

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Q.5 A hollow iron pipe is 21 cm long and its external diameter is 8 cm. If the thickness of the pipe is 1 cm and iron weighs 8 g/cm3, then the weight of the pipe is:

- 6 kg
- 696 kg
- 36 kg
- 9 kg

Ans. 2

Q.6 What is the volume of a cube?

I. The area of each face of the cube is 64 square metres.

II. The length of one side of the cube is 8 metres.

- I alone sufficient while II alone not sufficient to answer
- II alone sufficient while I alone not sufficient to answer
- Either I or II alone sufficient to answer
- Both I and II are not sufficient to answer

Ans. 3

Q.7 Find the surface area of a 10 cm × 4 cm × 3 cm brick.

- 128 sq. cm
- 164 sq. cm
- 194 sq. cm
- 208 sq. cm

Ans. 2

Q.8 What is the total surface area of a right circular cone of height 14 cm and base radius 7 cm?

- 35 cm2
- 462 cm2
- 35 cm2
- None of these

Ans. 3

Q.9 50 men took a dip in a water tank 40 m long and 20 m broad on a religious day. If the average displacement of water by a man is 4 m3, then the rise in the water level in the tank will be:

- 20 cm
- 25 cm
- 35 cm
- 50 cm

Ans. 2

Q.10 A right triangle with sides 3 cm, 4 cm and 5 cm is rotated the side of 3 cm to form a cone. The volume of the cone so formed is:

- 12 cm3
- 15 cm3
- 16 cm3
- 20 cm3

Ans. 1

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Q.11 66 cubic centimetres of silver is drawn into a wire 1 mm in diameter. The length of the wire in metres will be:

- 84
- 90
- 168
- 336

Ans. 1

Q.12 If the lateral surface of a cylinder is developed in a square whose diagonal is Ö2 cm long, then the volume of the cylinder in cubic centimeters is…….

- 1/4 π
- 2/ π
- 3 π/4
- 2 π

Ans . 1

Q.13 If a solid metal cylinder of radius 4 cm and height 10 cm, is melted to make solid balls of radius 1 mm, then number of such balls produced (in lakhs) will be.

- 8 lakh
- lakh
- lakh
- 4 lakh

Ans . 3

Q.14 If side of a square is 4 m, then area of the square in m² drawn on its diagonal is….

- 16
- 32
- 16Ö2
- 32Ö2

Ans. 2

Q.15 A plot of land is the shape of a right angled isosceles triangle. Length of the hypotenuse side is 50Ö2 and cost of the fencing is Rs. 3 per meter. The cost of fencing the plot will be.

- 381
- 341
- 391
- 371

Ans. 2

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Q.16 A reservoir is in the shape of a frustum of a right circular cone. It is 8 cm across at the top and 4 cm across at the bottom. It is 6 cm deep. Its capacity is.

- 176 m³
- 186 m³
- 88 m³
- 93 m³

Ans. 1

Q.17 30 Length of the longest rod that can be placed in a room 30 m long, 25 m broad and 18 m high is….

- 30 m
- 15 Ö2
- 60 m
- 30 Ö2 m

Ans . 4

Q.18 If a spherical lead of radius 20 cm is melted and small lead balls of radius 2 cm are made, then the total number of possible small lead balls is….

- 8000
- 800
- 80
- 100

Ans. 4

Q.19 A gold bar in the shape of a rectangular solid, 36 cm long, 9 cm broad and 6 cm high, is to be melted and cast into two different cubes, the volume the bigger being eight times that of the smaller. The surface is of the smaller cube, in cm² is….

- 36
- 216
- 72
- 144

Ans. 2

Q.20 A plane is drawn parallel to the base of a right circular cone dividing the altitude in the ratio of 2: 1 to chop off the conical part. The chopped off conical part is taller than the remaining portion. The ratio of the volumes of the chopped off part and the remaining part is….

- 1: 26
- 2: 25
- 4: 23
- 8: 19

Ans. 4

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