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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 triangle ABC, AD, BE and CF are the medians intersecting at point G and area of triangle ABC is 156 sq.cm. What is the area (in sq.cm) of triangle FGE?

A) 13 B) 26
C) 39 D) 52
 
Answer & Explanation Answer: A) 13

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0 1328
Q:

Volume of a cube is 512 cubic cm, find its total surface area? (Take π = 22/7)

A) 768 sq cms B) 192 sq cms
C) 384 sq cms D) 576 sq cms
 
Answer & Explanation Answer: C) 384 sq cms

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1 1324
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 1321
Q:

A cone of radius 7 cm and height 12 cm is completely filled with water. This water is emptied into an empty cylindrical vessel of radius 3.5 cm. What will be the height of water in this vessel?

A) 16 cm B) 32 cm
C) 5.33 cm D) 8 cm
 
Answer & Explanation Answer: A) 16 cm

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0 1319
Q:

If the areas of two similar triangle are in the ratio 5 : 7, then what is the ratio of the corresponding sides of these two triangles?

A) 5 : 7 B) 25 : 49
C) √5 : √7 D) 125 : 343
 
Answer & Explanation Answer: C) √5 : √7

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0 1316
Q:

If PA and PB are two tangents to a circle with centre O such that ∡APB = 80°. Then ∡AOP = 

A) 40° B) 50°
C) 60° D) 70°
 
Answer & Explanation Answer: B) 50°

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0 1314
Q:

If curved surface area of a cylinder is 616 sq cm and height is 14 cm, find its radius?

A) 14 cm B) 7 cm
C) 21 cm D) 3.5 cm
 
Answer & Explanation Answer: B) 7 cm

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0 1311
Q:

An inverted conical shaped vessel is filled with water to its brim. The height of the vessel is 8 cm and radius of the open end is 5 cm . When a few solid spherical metallic balls each of radius 1⁄2 cm are dropped in the vessel , 25% water is overflowed. The number of balls is:

A) 100 B) 400
C) 200 D) 150
 
Answer & Explanation Answer: A) 100

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0 1309