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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, ∠QPR = 45° and the bisectors of ∠PQR and ∠PRQ meets at O. What is the value (in degrees) of ∠QOR?

A) 107.5 B) 112.5
C) 117.5 D) 122.5
 
Answer & Explanation Answer: B) 112.5

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2 1000
Q:

Find the total surface area (in cm²) of a right circular cylinder of diameter 42 cm and height 14 cm

A) 4488 B) 4250
C) 4010 D) 4620
 
Answer & Explanation Answer: D) 4620

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0 1000
Q:

If the length of a chord of a circle is equal to that of the radius of the circle, then the angle subtended, in radians, at the centre of the circle by chord is

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

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0 995
Q:

The diagonal of a square is equal to the side of an equilateral triangle. If the area of the square is 15√3 sq cm, what is the area of the equilateral triangle?

A) 45/√2 sq cm B) 45√2 sq cm
C) 45 sq cm D) 45/2 sq cm
 
Answer & Explanation Answer: D) 45/2 sq cm

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1 993
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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0 993
Q:

The length of the diagonal and the breadth of a rectangle are 17 cm and 8 cm respectively. Find its perimeter (in cm).

A) 92 B) 46
C) 42 D) 84
 
Answer & Explanation Answer: B) 46

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0 992
Q:

A right circular cylinder is partially filled with water. Two iron spherical balls are completely immersed in the water so that the height of the water in the cylinder rises by 4 cm. If the radius of one ball is half of the other and the diameter of the cylinder is 18 cm, then the radii of the spherical balls are

A) 6 cm and 12 cm B) 4 cm and 8 cm
C) 3 cm and 6 cm D) 2 cm and 4 cm
 
Answer & Explanation Answer: C) 3 cm and 6 cm

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0 990
Q:

The height and the total surface area of a right circular cylinder are 4 cm and 8π sq.cm. respectively. The radius of the base of cylinder is

A) (2√2 - 2) cm B) (2 - √2) cm
C) 2 cm D) √2 cm
 
Answer & Explanation Answer: A) (2√2 - 2) cm

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0 990