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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 diameter of a circle is equal to the side of the square. What is the area of the square if the area of the circle is 49π sq cm?

A) 196 sq cm B) 154 sq cm
C) 124 sq cm D) 98 sq cm
 
Answer & Explanation Answer: A) 196 sq cm

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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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Q:

In ΔABC, ∠B=90 deg and BC= √3 AB. Find the measurement of ∠A

A) 45 deg B) 90 deg
C) 30 deg D) 60 deg
 
Answer & Explanation Answer: D) 60 deg

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Q:

In the given figure, PQR is a right angled triangle at Q. If PQ = 35 cm and QS = 28 cm, then what is the value (in cm) of SR?

A) 35.33 B) 37.33
C) 41.33 D) 43.33
 
Answer & Explanation Answer: B) 37.33

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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:

Radius of cross section of a solid right circular cylindrical rod is 3.2 dm. The rod is melted and 44 equal solid cubes of side 8 cm are formed. The length of the rod is (Take Π = 22/7)

A) 56 cm B) 7 cm
C) 5.6 cm D) 0.7 cm
 
Answer & Explanation Answer: B) 7 cm

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Q:

The perimeter and the breadth of a rectangle are 44 cm and 10 cm respectively. Find its area (in cm2).

A) 60 B) 240
C) 120 D) 180
 
Answer & Explanation Answer: C) 120

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Q:

Which of the following is not true for a rhombus?

A) All sides are congruent B) Opposite sides are parallel
C) Diagonals are equal D) Diagonals bisect each other at right angles
 
Answer & Explanation Answer: C) Diagonals are equal

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