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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 length of diagonal of a square is 9√2 cm. The square is reshaped to form a triangle. What is the area (in sq.cm) of largest in circle that can be formed in that triangle?

A) 6π B) 9π
C) 12π D) 15π
 
Answer & Explanation Answer: C) 12π

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Q:

The measure of the four successive angles of a quadrilateral are in the ratio 7 : 11 : 7 : 11. The quadrilateral is a ______.

A) trapezium B) rectangle
C) parallelogram D) square
 
Answer & Explanation Answer: C) parallelogram

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Q:

In ΔPQR, PQ = PR = 18 cm, AB and AC are parallel to lines PR and PQ respectively. If A is the mid-point of QR, then what is the perimeter (in cm) of quadrilateral ABPC?

A) 18 B) 28
C) 32 D) 36
 
Answer & Explanation Answer: D) 36

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Q:

The radius of base of a solid cylinder is 7 cm and its height is 21 cm. It is melted and converted into small bullets. Each bullet is of same size. Each bullet consisted of two parts viz. a cylinder and a hemisphere on one of its base. The total height of bullet is 3.5 cm and radius of base is 2.1 cm. Approximately how many complete bullets can be obtained?

A) 83 B) 89
C) 74 D) 79
 
Answer & Explanation Answer: A) 83

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Q:

Due to increase of k% in the side, the area of a square increases by 69%. What is the value of k?

A) 30 B) 33
C) 34.5 D) 35
 
Answer & Explanation Answer: A) 30

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Q:

A right circular solid cylinder has radius of base 7 cm and height is 28 cm. It is melted to form a cuboid such that the ratio of its side is 2 : 3 : 6. What is the total surface area (in cm2) cuboid?

A) 215633 B) 215693
C) 214833 D) 204833
 
Answer & Explanation Answer: B) 215693

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Q:

In ΔPQR, S and T are points on side PQ and PR respectively. ST is parallel to QR. If lengths of PS, SQ and PR are 6 cm, 9 cm and 12.5 cm respectively, what is the length of TR?

A) 7.5 cm B) 5 cm
C) 10 cm D) 2.5 cm
 
Answer & Explanation Answer: A) 7.5 cm

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Q:

In the given figure, PQRS is a square and SRT is an equilateral triangle. What is the value (in degrees) of angle SOR?

A) 45 B) 55
C) 60 D) 75
 
Answer & Explanation Answer: D) 75

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