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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 sphere and a solid hemisphere have the same total surface area. The ratio of their volumes is (Take, π=22/7)

A) 3√3 : 4 B) 4 : 3√3
C) 3 : 4√3 D) 1 : 12√3
 
Answer & Explanation Answer: A) 3√3 : 4

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Q:

Two circles are drawn with the same centre. The circumference of the smaller circle is 44 cm and that of the bigger circle is double the smaller one. What is the area between these two circles?A. 154 square cmB. 308 square cmC. 462 square cmD. 616 square cm

A) 154 square cm B) 308 square cm
C) 462 square cm D) 616 square cm
 
Answer & Explanation Answer: C) 462 square cm

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0 931
Q:

The ratio of curved surface area of a right circular cylinder to the total area of its two bases is 2 : 1. If the total surface area of cylinder is 23100 cm2, then what is the volume (in cm3) of cylinder?

A) 247200 B) 269500
C) 312500 D) 341800
 
Answer & Explanation Answer: B) 269500

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0 930
Q:

In a triangle the length of the side opposite the angle which measures 45° is 8 cm, what is the length of the side opposite to the angle which measures 90°?

A) 8√2 cm B) 4√2 cm
C) 8√3 cm D) 4√3 cm
 
Answer & Explanation Answer: A) 8√2 cm

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0 929
Q:

Δ ABC is right angled at B. If m∠A = 30°. What is the length (in cm) of AB, if AC = 8 cm?

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

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1 929
Q:

Δ XYZ is right angled at Y. If m∠Z = 30°. What is the length of YZ (in cm), if ZX = 9 cm?

A) 6√3 B) 9√3/2
C) 3√3 D) 18
 
Answer & Explanation Answer: B) 9√3/2

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0 928
Q:

The radius of a hemisphere is 7 cm, find its volume?

A) 718.67 cubic cm B) 1437.34 cubic cm
C) 239.56 cubic cm D) 359.34 cubic cm
 
Answer & Explanation Answer: A) 718.67 cubic cm

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0 927
Q:

Find the volume (in cm3) of a cube of side 7.5 cm.

A) 421.875 B) 77.145
C) 39.245 D) 24.435
 
Answer & Explanation Answer: A) 421.875

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0 926