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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:

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 1441
Q:

PQ and RS are common tangents to two circles intersecting at A and B. AB, when produced both sides, meet the tangents PQ and RS at X and Y, respectively. If AB = 3 cm, XY = 5 cm, then PQ (in cm) will be

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

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0 1440
Q:

A spherical glass vessel has a cylindrical neck 7 cm long and 4 cm in diameter. The diameter of the spherical part is 21 cm. Find the quantity of water it can hold.

 

A) 4929 cub.cm B) 4939 cub.cm
C) 4932 cub.cm D) 4930 cub.cm
 
Answer & Explanation Answer: B) 4939 cub.cm

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2 1440
Q:

The ratio of curved surface area of a right circular cylinder to the total area of its two bases is 2 : 1. If the total surface area of cylinder is 23100 cm2, then what is the volume (in cm3) of cylinder?

A) 247200 B) 269500
C) 312500 D) 341800
 
Answer & Explanation Answer: B) 269500

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0 1439
Q:

The perimeter and the breadth of a rectangle are 44 cm and 10 cm respectively. Find its area (in cm2).

A) 60 B) 240
C) 120 D) 180
 
Answer & Explanation Answer: C) 120

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0 1436
Q:

The two sides holding the right-angle in a right-angled triangle are 3 cm and 4 cm long. The area of its circumcircle will be in sq.cm:

A) 6.25pi B) 6.75pi
C) 5pi D) 7pi
 
Answer & Explanation Answer: A) 6.25pi

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0 1433
Q:

Find length of the arc whose central angle is 90° and radius of the circle is 3.5 cm?

A) 11 cm B) 5.5 cm
C) 16.5 cm D) 22 cm
 
Answer & Explanation Answer: B) 5.5 cm

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1 1433
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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