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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 point where the 3 medians of a triangle meet is called

A) centroid B) Incentre
C) Circumcentre D) orthocentre
 
Answer & Explanation Answer: A) centroid

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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 1376
Q:

If an equilateral triangle has side 12 cm, then what is the difference (in cm) between the circumradius and inradius?

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

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0 1372
Q:

If a cylinder of radius 7 cm and height 9 cm is melted and constructed into a cone of the same radius, what will be the height of this cone?

A) 54 cm B) 9 cm
C) 27 cm D) 13.5 cm
 
Answer & Explanation Answer: C) 27 cm

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0 1371
Q:

Three solid spheres of radius 3 cm, 4 cm and 5 cm are melted and recasted into a solid sphere. What will be the percentage decrease in the surface area?

A) 12 B) 14
C) 16 D) 28
 
Answer & Explanation Answer: D) 28

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1 1369
Q:

ABCD is a quadrilateral with AB = 9 cm, BC = 40 cm, CD = 28 cm, DA = 15 cm and angle ABC is a right –angel
What is the difference between perimeter of triangle ABC and perimeter of triangle ADC?

A) 4 cm B) 5 cm
C) 6 cm D) 7 cm
 
Answer & Explanation Answer: C) 6 cm

Explanation:
Perimeter of triangle ABC – Perimeter of triangle ADC = (9+40+41) - (15+28+41) = 6 cm
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Q:

PQ and RS are common tangents to two circles intersecting at A and B. AB, when produced both sides, meet the tangents PQ and RS at X and Y, respectively. If AB = 3 cm, XY = 5 cm, then PQ (in cm) will be

A) 3 cm B) 4 cm
C) 5 cm D) 2 cm
 
Answer & Explanation Answer: B) 4 cm

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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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