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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 radius of base of a solid cylinder is 7 cm and its height is 21 cm. It is melted and converted into small bullets. Each bullet is of same size. Each bullet consisted of two parts viz. a cylinder and a hemisphere on one of its base. The total height of bullet is 3.5 cm and radius of base is 2.1 cm. Approximately how many complete bullets can be obtained?

A) 83 B) 89
C) 74 D) 79
 
Answer & Explanation Answer: A) 83

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Q:

The surface areas of three faces of a cuboid sharing a vertex are 20, 32 and 40 sq. mts. What is the volume of the cuboid in cub. m?

A) √3024 B) 184
C) 160 D) 92
 
Answer & Explanation Answer: C) 160

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Q:

A right circular solid cylinder has radius of base 7 cm and height is 28 cm. It is melted to form a cuboid such that the ratio of its side is 2 : 3 : 6. What is the total surface area (in cm2) cuboid?

A) 215633 B) 215693
C) 214833 D) 204833
 
Answer & Explanation Answer: B) 215693

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Q:

Curved surface area of a cylinder is 1232 sq cm. If circumference of its base is 154 cm, then what will be the height of the cylinder? (Take π = 22/7)

A) 16 cm B) 4 cm
C) 8 cm D) 12 cm
 
Answer & Explanation Answer: C) 8 cm

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Q:

The total surface area of a hemisphere is 166.32 sq cm, find its radius?

A) 4.2 cm B) 8.4 cm
C) 1.4 cm D) 2.1 cm
 
Answer & Explanation Answer: A) 4.2 cm

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Q:

Two circles are having radii 9 cm and 12 cm. The distance between their centres is 15 cm. What is the length (in cm) of their common chord?

A) 6.8 B) 13.6
C) 7.2 D) 14.4
 
Answer & Explanation Answer: D) 14.4

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Q:

Three solid spheres have their radii r1, r2 and r3. The spheres are melted to form a solid sphere of bigger radius. Then the radius of the new sphere is

A) r1+r2+r3 B) r12+r22+r3212
C) r13+r23+r3313 D) r14+r24+r3414
 
Answer & Explanation Answer: C) r13+r23+r3313

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0 1207
Q:

BE and CF are two altitudes of a triangle ABC. If AB = 6 cm , AC = 5 cm and CF = 4 cm , then the length of BE is

A) 4.8 cm B) 7.5 cm
C) 3.33 cm D) 5.5 cm
 
Answer & Explanation Answer: A) 4.8 cm

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