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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:

A solid cube is cut into 27 identical cubes. What is the percentage increase in the total surface area?

A) 150 B) 200
C) 300 D) 250
 
Answer & Explanation Answer: B) 200

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0 1098
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 1095
Q:

In triangle PQR, A is the point of intersection of all the altitudes and B is the point of intersection of all the angle bisectors of the triangle. If ∠PBR =105°, then what is the value of ∠PAR (in degrees)?

A) 60 B) 100
C) 105 D) 115
 
Answer & Explanation Answer: A) 60

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0 1088
Q:

A solid has 12 vertices and 30 edges. How many faces does it have?

A) 22 B) 24
C) 26 D) 20
 
Answer & Explanation Answer: D) 20

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1 1075
Q:

The volume of a cube is 166.375 cm3. Find its side (in cm).

A) 6.5 B) 4.5
C) 7.5 D) 5.5
 
Answer & Explanation Answer: D) 5.5

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0 1074
Q:

A solid cone of height 36 cm and radius of base 9 cm is melted to form a solid cylinder of radius 9 cm and height 9 cm. What percent of material is wasted this process?

A) 25 B) 5
C) 0 D) 10
 
Answer & Explanation Answer: A) 25

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1 1067
Q:

Points P , Q and R are on a circle such that ∠PQR = 40° and ∠QRP = 60° . Then the subtended angle by arc QR at the centre is

A) 80° B) 120°
C) 140° D) 160°
 
Answer & Explanation Answer: D) 160°

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0 1066
Q:

In the given figure, ABCD is a square, BCXYZ is a regular pentagon and ABE is an  equilateral triangle. What is the value in deg of EBZ?

A) 102 B) 98
C) 78 D) 64
 
Answer & Explanation Answer: A) 102

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0 1065