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 Volume and Surface Area Questions

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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:

If 4r = h + r2+h2  then r: h = ? (r not equal to 0)

A) 17:8 B) 8:17
C) 8:15 D) 15:8
 
Answer & Explanation Answer: C) 8:15

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Q:

If the diameter of a hemisphere is 21 cm, then what is the volume (in cub.cm) of hemisphere?

A) 2810 B) 1250.5
C) 1725.25 D) 2425.5
 
Answer & Explanation Answer: D) 2425.5

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0 1045
Q:

If PQ and PR be the two tangents to a circle with centre O such that ∠QPR = 120° then ∠POQ is

A) 90° B) 45°
C) 30° D) 60°
 
Answer & Explanation Answer: C) 30°

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0 1042
Q:

In the given figure, PQR is a right angled triangle at Q. If PQ = 35 cm and QS = 28 cm, then what is the value (in cm) of SR?

A) 35.33 B) 37.33
C) 41.33 D) 43.33
 
Answer & Explanation Answer: B) 37.33

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0 1041
Q:

ΔXYZ is similar to ΔPQR. If ratio of Perimeter of ΔXYZ and Perimeter of ΔPQR is 16:9 and PQ = 3.6 cm, then what is the length(in cm) of XY?

A) 4.8 B) 3.2
C) 6.4 D) 8.6
 
Answer & Explanation Answer: C) 6.4

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0 1039
Q:

In the given figure, if AD = 12 cm, AE = 8 cm and EC = 14 cm, then what is the value of BD in cm?

A) 50/3 B) 15
C) 8/3 D) 44/3
 
Answer & Explanation Answer: C) 8/3

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2 1039
Q:

The ratio of the volume of two cylinders is 7 : 3 and the ratio of their heights is 7 : 9. If the area of the base of the second cylinder is 154 sq. cm, then what will be the radius (in cm) of the first cylinder?

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

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0 1036
Q:

The height of a right circular cylinder is twice its radius of the base. If its height be 6 times its radius of the base, then the volume of the cylinder will be 539 cub.cm more. Assuming Π = 22/7, the height of the cylinder is

A) 5 cm B) 7 cm
C) 9 cm D) 11 cm
 
Answer & Explanation Answer: B) 7 cm

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