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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:

From a solid cube of side 7 cm, a conical cavity of height 7 cm and radius 3 cm is hollowed out. Find the volume of remaining solid?

A) 272 cub.cm B) 270 cub.cm
C) 300 cub.cm D) 277 cub.cm
 
Answer & Explanation Answer: D) 277 cub.cm

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Q:

A cone of height 12 cm and diameter 10 cm is mounted on a hemisphere of the same diameter. What is the volume of the solid thus formed?

A) 384.13 sq cm B) 576.19 sq cm
C) 192.06 sq cm D) 288.1 sq cm
 
Answer & Explanation Answer: B) 576.19 sq cm

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0 820
Q:

In a triangle the length of the side opposite the angle which measures 60° is 6√3 cm. What is the length of the side opposite to the angle which measures 90°? 

A) 12√3 cm B) 6 cm
C) 12 cm D) 3√3 cm
 
Answer & Explanation Answer: C) 12 cm

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Q:

ΔABC is isosceles having AB = AC and ∠A = 40°. Bisectors PO and OQ of the exterior angles ∠ABD and ∠ACE formed by producing BC on both sides, meet at O. Then the value of ∠BOC is

A) 70° B) 110°
C) 80° D) 55°
 
Answer & Explanation Answer: A) 70°

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Q:

The volume of a sphere is 179.67 cub.cm. Find its diameter (in cm).

A) 3.5 B) 14
C) 7 D) 10.5
 
Answer & Explanation Answer: C) 7

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Q:

The co-ordinates of the centroid of a triangle ABC are (2 , 2). What are the co-ordinates of vertex C if co-ordinates of A and B are (7 , -1) and (1 , 2) respectively?

A) (-2 , 5) B) (2 , 5)
C) (-2 , -5) D) (2 , -5)
 
Answer & Explanation Answer: A) (-2 , 5)

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Q:

In an isosceles triangle ABC, AB = AC and ∠A = 80°. The bisector of ∠B and ∠C meet at D. The ∠BDC is equal to

A) 90° B) 100°
C) 130° D) 80°
 
Answer & Explanation Answer: C) 130°

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Q:

What are the co-ordinates of the centroid of a triangle, whose vertices are A(2 , 5), B(-4 , 0) and C(5 , 4)?

A) (-1 , 3) B) (1 , 3)
C) (1 , -3) D) (-1 , -3)
 
Answer & Explanation Answer: B) (1 , 3)

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