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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:

The cross section of a canal is in the shape of an isosceles trapezium which is 4 m wide at the bottom and 5 m wide at the top. If the depth of the canal is 2 m and it is 120 m long, what is the maximum capacity of this canal?

A) 2160 cubic mts B) 3240 cubic mts
C) 4320 cubic mts D) 1080 cubic mts
 
Answer & Explanation Answer: D) 1080 cubic mts

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Q:

A right prism has a square base with side of base 4 cm and the height of prism is 9 cm. The prism is cut in three parts of equal heights by two planes parallel to its base. What is the ratio of the volume of the top, middle and the bottom part respectively?

A) 1 : 8 : 27 B) 1 : 7 : 19
C) 1 : 8 : 20 D) no answer
 
Answer & Explanation Answer: D) no answer

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0 1294
Q:

In the given figure, in triangle STU, ST = 8 cm,TU = 9 cm and SU = 12 cm. QU = 24 cm, SR = 32 cm and PT = 27 cm. What is the ratio of the area of triangle PQU and area of triangle PTR?

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

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Q:

A right triangular pyramid XYZB is cut from cube as shown in figure. The side of cube is 16 cm. X, Y and Z are mid points of the edges of the cube. What is the total surface area (in sq.cm) of the pyramid?

 

A) 48[(√3) + 1] B) 24[4 + (√3)]
C) 28[6 + (√3)] D) 32[3 + (√3)]
 
Answer & Explanation Answer: D) 32[3 + (√3)]

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2 1289
Q:

ABCD is a rectangle. P is a point on the side AB as shown in the given figure. If Dp = 13, CP = 10

A) √105 B) √133
C) 12 D) 10
 
Answer & Explanation Answer: A) √105

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1 1283
Q:

In the given figure, MNOP is a square of side 6 cm. What is the value ( in cm ) of radius of circle?

A) 4.25 B) 3.75
C) 3.5 D) 4.55
 
Answer & Explanation Answer: B) 3.75

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0 1279
Q:

Volume of a cylinder is 770 cubic cm. If circumference of its base is 22 cm, what will be the curved surface area of the cylinder? (Take π = 22/7)

A) 440 sq cms B) 880 sq cms
C) 220 sq cms D) 660 sq cms
 
Answer & Explanation Answer: A) 440 sq cms

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1 1277
Q:

In a circle of radius 8 cm, AB and AC are two chords such that AB = AC = 12 cm. What is the length of chord BC?

A) 2√6 cm B) 3√6 cm
C) 3√7 cm D) 6√7 cm
 
Answer & Explanation Answer: D) 6√7 cm

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