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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:

Diameter of wheel of a cycle is 21 cm. The cyclist takes 45 minutes to reach a destination at a speed of 16.5 km/hr. How many revolutions will the wheel make during the journey?

A) 12325 B) 18750
C) 21000 D) 24350
 
Answer & Explanation Answer: B) 18750

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Q:

In the given figure, P  is the center of the circle. If QS = PR, then what is the ratio of angles RSP to the TPR ?

A) 1 : 4 B) 2 : 5
C) 1 : 3 D) 2 : 7
 
Answer & Explanation Answer: C) 1 : 3

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0 1128
Q:

ΔXYZ is similar to ΔPQR. If ratio of Perimeter of ΔXYZ and Perimeter of ΔPQR is 4:9 and if PQ = 27 cm, then what is the length of XY (in cm)?

A) 9 B) 12
C) 16 D) 15
 
Answer & Explanation Answer: B) 12

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Q:

An equilateral triangle of area 300 cm2 is cut from its three vertices to form a regular hexagon. Area of hexagon is what percent of the area of triangle?

A) 66.66% B) 33.33%
C) 83.33% D) 56.41%
 
Answer & Explanation Answer: A) 66.66%

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0 1127
Q:

The radius of two cylinders are in the ratio of 3:2 and their heights are in the ratio 3:7. The ratio of their volumes is :

A) 4:7 B) 7:4
C) 28:27 D) 27:28
 
Answer & Explanation Answer: D) 27:28

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Q:

Incentre of Δ ABC is I. ∠ABC = 90° and ∠ACB = 70°. ∠AIC is

A) 115° B) 100°
C) 110° D) 105°
 
Answer & Explanation Answer: C) 110°

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0 1119
Q:

Two circles touch externally. The sum of their areas is 130π sq.cm and the distance between their centers is 14 cm. The radius of the bigger circle is

A) 22 cm B) 11 cm
C) 33 cm D) 44 cm
 
Answer & Explanation Answer: B) 11 cm

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0 1119
Q:

ABCD is a quadrilateral with AB = 9 cm, BC = 40 cm, CD = 28 cm, DA = 15 cm and angle ABC is a right –angel. 
What is the area of triangle ADC?

A) 126 SQ.CM B) 124 SQ.CM
C) 122 SQ.CM   D) 120 SQ.CM
 
Answer & Explanation Answer: A) 126 SQ.CM

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