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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 radius and the height of a cone are each increased by 20%. Then the volume of the cone increases by

A) 20% B) 20.5%
C) 62% D) 72.8%
 
Answer & Explanation Answer: D) 72.8%

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Q:

The two equal sides of an isosceles triangle is 20 cm each and the third side is 30 cm. What is the area (in sq.cm) of the triangle?

A) 50√5 B) 100
C) 75√7 D) 175
 
Answer & Explanation Answer: C) 75√7

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Q:

A cylindrical vessel of radius 7 cm is partially filled with water. By how much will the water level rise if a sphere of radius 6 cm is completely immersed in this water?

A) 11.76 cm B) 17.64 cm
C) 23.52 cm D) 5.88 cm
 
Answer & Explanation Answer: D) 5.88 cm

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0 934
Q:

At what point does the line 3x + y = -6 intercept the x-axis?

A) (2,0) B) (-2,0)
C) (0,-6) D) (0,6)
 
Answer & Explanation Answer: B) (-2,0)

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Q:

What is the slope of the line parallel to the line passing through the points (5, -1) and (4, -4)?

A) -3 B) -1/3
C) 3 D) 1/3
 
Answer & Explanation Answer: C) 3

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0 931
Q:

The copper wire when bent in the form of a square encloses an area of 121 cub.cm. If the same wire is bent into the form of a circle, find the area of the circle.

A) 154 sq.cm B) 153 sq.cm
C) 155 sq.cm D) 150 sq.cm
 
Answer & Explanation Answer: A) 154 sq.cm

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Q:

Find the total surface area (in cm2) of a cube of side 3.5 cm.

A) 91.7 B) 64
C) 88 D) 73.5
 
Answer & Explanation Answer: D) 73.5

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Q:

The sum of the lengths of the edges of a cube is equal to half the perimeter of a square. If the numerical value of the volume pf the cube is equal to one-sixth of the numerical value of the area of the square, then the length of one side of the square is

A) 31.5 units B) 36 units
C) 27 units D) 18 units
 
Answer & Explanation Answer: B) 36 units

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