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 Volume and Surface Area Questions

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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 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:

A cylindrical vessel of radius 8 cm is partially filled with water. By how much will the water level rise if a sphere of radius 7 cm is completely immersed in this water?

A) 7.15 cm B) 14.3 cm
C) 21.45 cm D) 28.6 cm
 
Answer & Explanation Answer: A) 7.15 cm

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Q:

If the length of a chord of a circle is equal to that of the radius of the circle, then the angle subtended, in radians, at the centre of the circle by chord is

A) 1 B) ∏/2
C) ∏/3 D) ∏/4
 
Answer & Explanation Answer: C) ∏/3

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Q:

The base area of a right pyramid is 57 sq. units and height is 10 units. Then the volume of the pyramid is

A) 190 c. units B) 380 c. units
C) 540 c. units D) 570 c. units
 
Answer & Explanation Answer: A) 190 c. units

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Q:

What is the reflection of the point (5 , -1) in the line y = 2?

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

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Q:

If O is the centre of a circle of radius 5 cm. At a distance of 13 cm from O, a point P is taken. From this point, two tangents PQ and PR are drawn to the circle. Then , the area of quadrilateral PQOR is

A) 60 cm2 B) 32.5 cm2
C) 65 cm2 D) 30 cm2
 
Answer & Explanation Answer: A) 60 cm2

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Q:

A cylindrical capsule has hemispherical ends of the radii equal to radius of the cylindrical part. If length of the capsule is 40 m and radius 6 m, what is the total surface area of this capsule?

A) 3017.14 sq mts B) 4525.71 sq mts
C) 1508.57 sq mts D) 754.29 sq mts
 
Answer & Explanation Answer: C) 1508.57 sq mts

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Q:

A square is inscribed in a circle. If the side of the square is 14 cm, what is the area (in sq.cm) of the circle?

A) 49π B) 77π
C) 121π D) 98π
 
Answer & Explanation Answer: D) 98π

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