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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 ratio of total surface area and volume of a sphere is 1 : 7. This sphere is melted to form small spheres of equal size. The radius of each small sphere is 1/6th the radius of the large sphere. What is the sum (in cm2) of curved surface areas of all small spheres?

A) 31276 B) 36194
C) 25182 D) 33264
 
Answer & Explanation Answer: D) 33264

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Q:

An angle is greater than its complementary by 20°. What will be the measure of the angle?

A) 55° B) 35°
C) 100° D) 80°
 
Answer & Explanation Answer: A) 55°

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Q:

Triangle ΔXYZ is similar to ΔPQR. If XY:PQ=5:1. If Area of ΔPQR is 5 sq cm, what is the area (in sq cm) of ΔXYZ?

A) 125 B) 120
C) 100 D) 64
 
Answer & Explanation Answer: A) 125

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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:

Which of the set of three sides can't form a triangle?

A) 5 cm, 6 cm, 7 cm B) 5 cm, 8 cm, 15 cm
C) 8 cm, 15 cm, 18 cm D) 6 cm, 7 cm, 11 cm
 
Answer & Explanation Answer: B) 5 cm, 8 cm, 15 cm

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Q:

In triangle ABC, ∠ABC = 90°. BP is drawn perpendicular to AC. If ∠BAP = 30°, then what is the value (in degrees) of ∠PBC?

A) 30 B) 36
C) 45 D) 60
 
Answer & Explanation Answer: A) 30

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Q:

What must be the length (in cm) of the diagonal of a rectangle if its area and breadth are 120 sq.cm and 8 cm respectively ?

A) 34 B) 17
C) 15 D) 30
 
Answer & Explanation Answer: B) 17

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Q:

The triangle ABC and DEF are similar to each other. The measure of the angle A and E is 67 and 83 degree respectively. What is the value of angle C?

A) 20°   B) 30°
C) 40° D) 50°
 
Answer & Explanation Answer: B) 30°

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