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 Volume and Surface Area Questions

Popular Latest Rated Important Formulae

FACTS  AND  FORMULAE  FOR  VOLUME  AND  SURFACE  AREA  QUESTIONS

 

 

I. CUBOID

   Let length=l, breadth =b and height =h units. Then,

1. Volume = (l x b x h)

2. Surface area = 2(lb +bh + lh) sq.units

3. Diagonal =l2+b2+h2 units

 

 

II. CUBE 

Let each edge of a cube be of length a. Then,

1. Volume = a3 cubic units.

2. Surface area = 6a2 sq.units

3. Diagonal = 3a units

 

 

III. CYLINDER 

Let radius of base = r and Height (or Length) = h. Then, 

1.Volume = πr2h cubic units 

2. Curved surface area = 2πrh sq.units

3. Total surface area = 2πrh+2πr2 sq.units

 

 

IV. CONE 

Let radius of base =r and Height = h. Then, 

1. Slant height, l=h2+r2 units

 

2. Volume = 13πr2h cubic units.

 

3. Curved surface area = πrlsq.units 

 

4. Total surface area = πrl+πr2sq.units

 

 

V. SPHERE 

Let the radius of the sphere be r. Then, 

1. Volume =43πr3 cubic units

2. Surface area = 4πr2 sq.units

 

 

VI. HEMISPHERE 

Let the radius of a hemisphere be r. Then, 

1. Volume = 23πr3 cubic units.

2. Curved surface area = 2πr2 sq.units

3. Total surface area = 3πr2 sq.units

 

Q:

In the given figure, P  is the center of the circle. If QS = PR, then what is the ratio of angles RSP to the TPR ?

A) 1 : 4 B) 2 : 5
C) 1 : 3 D) 2 : 7
 
Answer & Explanation Answer: C) 1 : 3

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Q:

A right circular cylinder has height as 18 cm and radius as 7 cm. The cylinder is cut in three equal parts (by 2 cuts parallel to base). What is the percentage increase in total surface area?

A) 62 B) 56
C) 48 D) 52
 
Answer & Explanation Answer: B) 56

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0 1354
Q:

ABCD is a trapezium in which AB is parallel to CD and AB = 4(CD). The diagonals of the trapezium intersects at O. What is the ratio of area of triangle DCO to the area of the triangle ABO?

A) 1 : 4 B) 1 : 2
C) 1 : 8 D) 1 : 16
 
Answer & Explanation Answer: D) 1 : 16

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0 1353
Q:

The volume of metallic cylindrical pipe of uniform thickness is 748 c.c. Its length is 14 cm and its external radius is 9 cm. The thickness of the pipe is

A) 0.5 cm B) 1.5 cm
C) 1 cm D) 2 cm
 
Answer & Explanation Answer: C) 1 cm

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2 1351
Q:

ABC is a right angled triangle with angle A = 90 deg. Then the value of cos2A+cos2B+cos2C is

A) 2 B) 1
C) 0 D) 3
 
Answer & Explanation Answer: B) 1

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0 1348
Q:

O is the centre of the circle and ∠AOB = 150°, and the shaded portion is x part of the circular region, then x = ?

A) 1/12 B) 1/9
C) 1/6 D) 1/4
 
Answer & Explanation Answer: C) 1/6

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0 1347
Q:

The length, breadth and height of a cuboid are 12 cm, 8 cm and 6 cm respectively. The volume of the cuboid is (Use π = 22/7)

A) 1152 cubic cms B) 288 cubic cms
C) 576 cubic cms D) 864 cubic cms
 
Answer & Explanation Answer: C) 576 cubic cms

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0 1347
Q:

In a cyclic quadrilateral ABCD , the side AB is extended to a point X. If ∠XBC = 82° and ∠ADB = 47° , then the value of ∠BDC is

A) 40° B) 35°
C) 30° D) 25°
 
Answer & Explanation Answer: B) 35°

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