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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, 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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3 1445
Q:

ABC is a right angled triangle in which ∠A = 90°, AB = 5 cm and AC = 12 cm. What is the approximate volume (in cm3) of the double cone formed by rotating the triangle about its hypotenuse?

A) 145 B) 290
C) 435 D) 580
 
Answer & Explanation Answer: B) 290

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1 1442
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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0 1440
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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0 1439
Q:

If the lengths of two parallel chords in a circle of radius 10 cm are 12 cm and 16 cm, then what is the distance between these two chords?

A) 1 cm or 7 cm B) 2 cm or 14 cm
C) 3 cm or 21 cm D) 4 cm or 28 cm
 
Answer & Explanation Answer: B) 2 cm or 14 cm

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1 1436
Q:

BE and CF are two altitudes of a triangle ABC. If AB = 6 cm , AC = 5 cm and CF = 4 cm , then the length of BE is

A) 4.8 cm B) 7.5 cm
C) 3.33 cm D) 5.5 cm
 
Answer & Explanation Answer: A) 4.8 cm

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1 1433
Q:

Curved surface area of a cylinder is 1232 sq cm. If circumference of its base is 154 cm, then what will be the height of the cylinder? (Take π = 22/7)

A) 16 cm B) 4 cm
C) 8 cm D) 12 cm
 
Answer & Explanation Answer: C) 8 cm

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1 1431
Q:

10 identical solid spherical balls of radius 3 cm are melted to form a single sphere. In this process 20% of solid is wasted. What is the radius (in cm) of the bigger sphere?

A) 24 B) 12
C) 8 D) 6
 
Answer & Explanation Answer: D) 6

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