**Volume and Surface Area**

Check all important Volume and Surface Area Formulas for solving the problems. Read the definition and know about the tricks and strategies to solve **Volume and Surface Area** Questions and Answers in an easy way. Selective Multiple Choice Questions and Answers of Volume and Surface Area Topic are given here, so that candidates can have a basic idea of the types of questions that are asked in the examination.

**Volume and Surface Area**

**Volume and Surface Area Definition:**

**Surface Area:**

- The space occupied by a two-dimensional flat surface is called the area. It is measured in square units.
- The area occupied by a three-dimensional object by its outer surface is called surface area. It is also measured in square units.

__Area can be of two types__:

(i) Total Surface Area

(ii) Curved Surface Area/Lateral Surface Area

(i) __Total Surface Area__:

Total surface area refers to the area including the base(s) and the curved part. It is total of the area covered by the surface of the object. If the shape has curved surface and base, then total area will be the sum of the two areas.

(ii) __Curved Surface Area/Lateral Surface Area__:

Curved surface area refers to the area of only the curved part of the shape excluding its base(s). It is also referred to as lateral surface area for shapes such as a cylinder.

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**Volume:**

The amount of space, measured in cubic units, that an object or substance occupies is called volume. Two-dimensional doesn’t have volume but has area only. Example, Volume of Circle cannot be found, though Volume of the sphere can be. It is so because a sphere is a three-dimensional shape.

**Volume and Surface Area Important Formula:**

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**Volume and Surface Area Tricks:**

**1) For a closed wooden box:**

(i) Capacity = (external length – 2 x thickness) x (external breadth – 2 x thickness) x (external height – 2 x thickness)

(ii) Volume of material = External volume – capacity

(iii) Weight of wood = Volume of wood x density of wood.

**2) Problems involving ratios:**

** Two Spheres:**

(i) (Ratio of radii)^{2} = ratio of surface areas.

(ii) Ratio of volumes = (ratio of radii)^{3}

(iii) (Ratio of surface areas)^{3} = (ratio of volumes)^{2}

** Two cylinders:**

When the radii are equal:

(i) Ratio of volumes = ratio of heights.

(ii) Ratio of curved surface areas = ratio of heights

(iii) Ratio of volumes = (ratio of curved surface areas)

When heights are equal:

(i) Ratio of volumes = (ratio of radii)^{2}

(ii) Ratio of curved surface areas = ratio of radii

(iii) Ratio of volumes = (ratio of curved surface areas)^{2}

When volumes are equal:

(i) Ratio of radii

(ii) Ratio of curved surface areas

When curved surface areas are equal:

(i) Ratio of volumes = ratio of radii

(ii) Ratio of volumes = inverse ratio of heights.

(iii) Ratio of radii = inverse ratio of heights.

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**Volume and Surface Area Problems:**

**Question 1)** If each edge of a cube is increased by 50%, find the percentage increase in Its surface area

A) 125%

B) 150%

C) 175%

D) 110%

**Question 2)** A rectangular block 6 cm by 12 cm by 15 cm is cut up into an exact number of equal cubes. Find the least possible number of cubes.

A) 30

B) 40

C) 10

D) 20

**Question 3)** 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:

A) 720

B) 900

C) 1200

D) 1800

**Question 4)** The diagonal of a rectangle is sqrt(41) cm. and its area is 20 sq. cm. The perimeter of the rectangle must be:

A) 9 cm

B) 18 cm

C) 20 cm

D) 41 cm

**Question 5)** 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:

A) 12 pi cub.cm

B) 15 pi cub.cm

C) 16 pi cub.cm

D) 20 pi cub.cm

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**Question 6)** 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 cu.m , then the rise in the water level in the tank will be:

A) 20 cm

B) 25 cm

C) 35 cm

D) 50 cm

**Question 7) **A cistern 6m long and 4 m wide contains water up to a depth of 1 m 25 cm. The total area of the wet surface is:

A) 49

B) 50

C) 53.5

D) 55

**Question 8) **How many cubes of 3cm edge can be cut out of a cube of 18cm edge

A) 36

B) 232

C) 216

D) 484

**Question 9) **Three solid cubes of sides 1 cm, 6 cm and 8 cm are melted to form a new cube. Find the surface area of the cube so formed

A) 486

B) 586

C) 686

D) 786

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**Question 10) **Find the length of the longest pole that can be placed in a room 12 m long 8m broad and 9m high.

A) 14m

B) 15m

C) 16m

D) 17m

**Answers:**

Ans1) (A) | Ans6) (B) |

Ans2) (B) | Ans7) (A) |

Ans3) (C) | Ans8) (C) |

Ans4) (B) | Ans9) (A) |

Ans5) (A) | Ans10) (D) |

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