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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:

PQ and RS are common tangents to two circles intersecting at A and B. AB, when produced both sides, meet the tangents PQ and RS at X and Y, respectively. If AB = 3 cm, XY = 5 cm, then PQ (in cm) will be

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

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0 1033
Q:

In ΔABC, ∠BAC = 90° and AD is drawn perpendicular to BC. If BD = 7 cm and CD = 28 cm, then what is the length (in cm) of AD?

A) 3.5 B)  7
C) 10.5 D) 14
 
Answer & Explanation Answer: D) 14

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0 1029
Q:

The total surface area of a cuboid is 376 sq cm. Find its volume if its length and breadth are 10 cm and 8 cm respectively?

A) 960 cubic cms B) 240 cubic cms
C) 480 cubic cms D) 720 cubic cms
 
Answer & Explanation Answer: C) 480 cubic cms

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0 1028
Q:

ΔABC is similar to ΔPQR. Length of AB is 18 cm and length of the corresponding side PQ is 12 cm. If area of ΔABC is 324 sq cm, what is the area of ΔPQR?

A) 72 sq cm B) 144 sq cm
C) 36 sq cm D) 487.5 sq cm
 
Answer & Explanation Answer: B) 144 sq cm

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0 1027
Q:

The radius of the circle circumscribing the three vertices of an equilateral triangle is 12 cm. Determine the height (in cm) of the equilateral triangle

A) 12 B) 14
C) 18 D) 20
 
Answer & Explanation Answer: C) 18

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4 1026
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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1 1025
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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0 1025
Q:

In triangle ABC, a line is drawn from the vertex A to a point D on BC. If BC = 9 cm and DC = 3 cm, then what is the ratio of the areas of triangle ABD and triangle ADC respectively?

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

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0 1023