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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 ΔPQR, S and T are points on side PQ and PR respectively. ST is parallel to QR. If lengths of PS, SQ and PR are 6 cm, 9 cm and 12.5 cm respectively, what is the length of TR?

A) 7.5 cm B) 5 cm
C) 10 cm D) 2.5 cm
 
Answer & Explanation Answer: A) 7.5 cm

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1 1771
Q:

Curved surface area of a cylinder is 1232 sq cm. If circumference of its base is 154 cm, then what will be the height of the cylinder? (Take π = 22/7)

A) 16 cm B) 4 cm
C) 8 cm D) 12 cm
 
Answer & Explanation Answer: C) 8 cm

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1 1767
Q:

If the lengths of two parallel chords in a circle of radius 10 cm are 12 cm and 16 cm, then what is the distance between these two chords?

A) 1 cm or 7 cm B) 2 cm or 14 cm
C) 3 cm or 21 cm D) 4 cm or 28 cm
 
Answer & Explanation Answer: B) 2 cm or 14 cm

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1 1759
Q:

D, E, F are the mid - points of the sides BC , CA and AB respectively of a ΔABC . Then the ratio of the areas of ΔDEF and ΔABC is

A) 1/2 B) 1/4
C) 1/8 D) 1/16
 
Answer & Explanation Answer: B) 1/4

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0 1757
Q:

The total surface area of a hemisphere is 4158 cm2. Find its diameter (in cm).

A) 21 B) 84
C) 42 D) 63
 
Answer & Explanation Answer: B) 84

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2 1754
Q:

Three consecutive integers form the lengths of a right-angled triangle. How many sets of such three consecutive integers is/are possible?

A) Only one B) Only two
C) Only three D) Infinitely many
 
Answer & Explanation Answer: A) Only one

Explanation:

let n-1, n, n+1 be 3 consecutive integers

So

(n+1)^2= n^2+ (n-1)^2

(n+1)^2-(n-1)^2= n^2

4n = n^2

So n = 0 or n = 4

n can’t be 0 as n-1 will be negative then

So 3,4 and 5 is the only triplet formed.

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0 1752
Q:

ABC is a right angled triangle in which ∠A = 90°, AB = 5 cm and AC = 12 cm. What is the approximate volume (in cm3) of the double cone formed by rotating the triangle about its hypotenuse?

A) 145 B) 290
C) 435 D) 580
 
Answer & Explanation Answer: B) 290

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1 1750
Q:

The radius of base of a solid cylinder is 7 cm and its height is 21 cm. It is melted and converted into small bullets. Each bullet is of same size. Each bullet consisted of two parts viz. a cylinder and a hemisphere on one of its base. The total height of bullet is 3.5 cm and radius of base is 2.1 cm. Approximately how many complete bullets can be obtained?

A) 83 B) 89
C) 74 D) 79
 
Answer & Explanation Answer: A) 83

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1 1749