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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:

How many balls of radius 2 cm can be made by melting a bigger ball of diameter 16 cm? (Take π = 22/7)

A) 64 B) 128
C) 32 D) 96
 
Answer & Explanation Answer: A) 64

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Q:

The length of the common chord of two intersecting circles is 12 cm. If the diameters of the circles are 15 cm and 13 cm, then what is the distance (in cm) between their centers?

A) 7/2 B) 7
C) 7√2 D) 14
 
Answer & Explanation Answer: B) 7

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Q:

ΔXYZ is similar to ΔPQR. If ratio of Perimeter of ΔXYZ and Perimeter of ΔPQR is 16:9 and PQ = 3.6 cm, then what is the length(in cm) of XY?

A) 4.8 B) 3.2
C) 6.4 D) 8.6
 
Answer & Explanation Answer: C) 6.4

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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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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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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:

In a triangle ABC, OB and OC are the bisectors of angles ∠ B and ∠C respectively. ∠BAC = 60°. Then the angle ∠BOC will be

A) 150° B) 120°
C) 100° D) 90°
 
Answer & Explanation Answer: B) 120°

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Q:

If the difference between the measures of the two smaller angles of a right angled triangle is 8°, then the smallest angle is

A) 37° B) 41°
C) 42° D) 49°
 
Answer & Explanation Answer: B) 41°

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