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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:

Thousand solid metallic spheres of diameter 6 cm are melted and recast into a new solid sphere. The diameter of the new sphere (in cm) is

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

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Q:

A solid sphere and a solid hemisphere have the same total surface area. The ratio of their volumes is (Take, π=22/7)

A) 3√3 : 4 B) 4 : 3√3
C) 3 : 4√3 D) 1 : 12√3
 
Answer & Explanation Answer: A) 3√3 : 4

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Q:

In triangle ABC, ∠ABC = 90°. BP is drawn perpendicular to AC. If ∠BAP = 50°, then what is the value (in degrees) of ∠PBC?

A) 30 B) 45
C) 50 D) 60
 
Answer & Explanation Answer: C) 50

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0 1041
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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Q:

In triangle ABC, O is the orthocenter and angle BOC is 120 deg. Calculate angle BAC.

A) 30 deg B) 40 deg
C) 60 deg D) 80 deg
 
Answer & Explanation Answer: C) 60 deg

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Q:

If O is the centre of a circle of radius 5 cm. At a distance of 13 cm from O, a point P is taken. From this point, two tangents PQ and PR are drawn to the circle. Then , the area of quadrilateral PQOR is

A) 60 cm2 B) 32.5 cm2
C) 65 cm2 D) 30 cm2
 
Answer & Explanation Answer: A) 60 cm2

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0 1032
Q:

The area of a triangle ABC is 63 sq.units. Two parallel lines DE, FG, are drawn such that they divide the line segments AB and AC into three equal parts. What is the area of the quadrilateral DEGF?

 

 

A) 28 sq.units B) 35 sq.units
C) 21 sq.units D) 48 sq.units
 
Answer & Explanation Answer: C) 21 sq.units

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1 1031
Q:

What is the diameter (in cm) of a sphere of surface area 154 sq cm?

A) 3.5 B) 14
C) 10.5 D) 7
 
Answer & Explanation Answer: D) 7

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