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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:

 In ΔDEF measure of angle E is 90 deg. If tanD = 4/3, and DE = 6cm, then what is the length (in cm) of side EF?

A) 10 B) 5
C) 8 D) 4
 
Answer & Explanation Answer: C) 8

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0 831
Q:

In a triangle the length of the side opposite the angle which measures 30 degree is 9√3 cm, what is the length of the side opposite to the angle which measures 60 degree?

A) 27 cm B) 9 cm
C) 12√3 cm D) (15√3)/2 cm
 
Answer & Explanation Answer: A) 27 cm

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0 829
Q:

If the side of the equilateral triangle is 8√3 cm, then what is the length (in cm) of the in radius of the triangle?

A) 2 B) 4
C) 8√3 D) 16√3
 
Answer & Explanation Answer: B) 4

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0 828
Q:

The lengths of two parallel sides of a trapezium are 21 cm and 9 cm. If its height is 10 cm, then what is the area (in cm2) of the trapezium?

A) 35 B) 75
C) 150 D) 225
 
Answer & Explanation Answer: C) 150

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0 827
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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0 827
Q:

Possible length of the three sides of a triangle are :­

A) 2 cm , 3 cm , 6 cm B) 3 cm , 4 cm , 5 cm
C) 2.5 cm , 3.5 cm , 6 cm D) 4 cm , 4 cm , 9 cm
 
Answer & Explanation Answer: B) 3 cm , 4 cm , 5 cm

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0 826
Q:

Two circles touch each other at point X. Two common tangents of the circles meet at point P and none of the tangents passes through X. These tangents touch the larger circle at points B and C. If the radius of the larger circle is 15 cm and CP = 20 cm, then what is the radius (in cm) of the smaller circle?

A) 3.5 B) 3.75
C) 4.25 D) 4.45
 
Answer & Explanation Answer: B) 3.75

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0 826
Q:

The side BC of ΔABC is produced to D. If ∠ACD = 114° and ∠ABC= (1/2)∠BAC, then what is the value (in degrees) of ∠BAC?

A) 36 B) 48
C) 76 D) 84
 
Answer & Explanation Answer: C) 76

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0 825