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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:

Points P and Q lie on side AB and AC of triangle ABC respectively such that segment PQ is parallel to side BC. If the ratio of AP:PB is 1:4 and area of Δ APQ is 4 sq cm, what is the area of trapezium PQCB?

A) 60 sq cm B) 16 sq cm
C) 96 sq cm D) 21 sq cm
 
Answer & Explanation Answer: C) 96 sq cm

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Q:

What is the equation of the line perpendicular to the line 2x + 3y= -6 and having Y-intercept 3?

A) 3x - 2y = 6 B) 3x - 2y = -6
C) 2x - 3y = -6 D) 2x - 3y = 6
 
Answer & Explanation Answer: B) 3x - 2y = -6

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0 1093
Q:

Triangle ΔXYZ is similar to ΔPQR. If XY:PQ=5:1. If Area of ΔPQR is 5 sq cm, what is the area (in sq cm) of ΔXYZ?

A) 125 B) 120
C) 100 D) 64
 
Answer & Explanation Answer: A) 125

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0 1092
Q:

If the circum radius of the equilateral triangle is 12 cm then what is the value of in radius (in cm) of the triangle?

A) 3 B) 6
C) 8 D) 10
 
Answer & Explanation Answer: B) 6

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1 1091
Q:

In a triangle the length of the side opposite the angle which measures 60° is 6√3 cm. What is the length of the side opposite to the angle which measures 90°? 

A) 12√3 cm B) 6 cm
C) 12 cm D) 3√3 cm
 
Answer & Explanation Answer: C) 12 cm

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1 1089
Q:

What is the area (in sq cm) of a regular hexagon of side 14 cm?

A) 147√3 B) 441√3
C) 196√3 D) 294√3
 
Answer & Explanation Answer: D) 294√3

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0 1089
Q:

A cone is hollowed out of a solid wooden cube of side 6 cm. The diameter and height of the cone is same as the side of the cube. What is the volume of the remaining cube?

A) 159.42 cubic cms B) 323.15 cubic cms
C) 106.33 cubic cms D) 210.66 cubic cms
 
Answer & Explanation Answer: A) 159.42 cubic cms

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0 1089
Q:

In a right angled triangle ΔDEF, if the length of the hypotenuse EF is 12 cm, then the length of the median DX is

A) 3 cm B) 4 cm
C) 6 cm D) 12 cm
 
Answer & Explanation Answer: C) 6 cm

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0 1088