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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 volume of a right circular cone, with a base radius the same as its altitude, and the volume of a hemisphere are equal. The ratio of the radii of the cone to the hemisphere is

A) 2 : 1 B) √2 : 1
C) 23 : 1 D) 33 : 23
 
Answer & Explanation Answer: C) 23 : 1

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Q:

What is the reflection of the point (-1 , 3) in the line x = -4?

A) (-7 ,-3) B) (-7 ,3)
C) (7 ,-3) D) (7 ,3)
 
Answer & Explanation Answer: B) (-7 ,3)

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Q:

An angle is greater than its complementary angle by 40°. Find the measure of the angle?

A) 25° B) 65°
C) 130° D) 50°
 
Answer & Explanation Answer: B) 65°

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Q:

The diameter of the driving wheel of a cart is 154 cm. Calculate the revolution per minute [RPM] of the wheel in order to keep a speed of 33 kmph?

A) 114 B) 112
C) 110 D) 108
 
Answer & Explanation Answer: A) 114

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Q:

The length of the diagonal and the breadth of a rectangle are 29 cm and 20 cm respectively. Find its perimeter (in cm).

 

A) 164 B) 82
C) 21 D) 42
 
Answer & Explanation Answer: B) 82

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Q:

O is an centre of a circle. P is an external point of it at distance of 13cm from O. The radius of the circle is 5cm. Then the length of a tangent to the circle from P upto the point of contact is

A) √194cm B) 10cm
C) 12cm D) 8cm
 
Answer & Explanation Answer: C) 12cm

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Q:

D and E are points on side AB and AC of ΔABC. DE is parallel to BC. If AD:DB = 1:2 and area of ΔABC is 45 sq cm, what is the area (in sq cm) of quadrilateral BDEC?

A) 20 B) 40
C) 15 D) 30
 
Answer & Explanation Answer: B) 40

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Q:

The co-ordinates of the centroid of a triangle ABC are (1 , -4). What are the co-ordinates of vertex C if co-ordinates of A and B are (3 , -4) and (0 , 5) respectively?

A) (0 , 13) B) (0, 5)
C) (0, -5) D) (0 , -13)
 
Answer & Explanation Answer: D) (0 , -13)

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