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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:

A cube is inscribed in a sphere. A right circular cylinder is within the cube touching all the vertical faces. A right circular once is inside the cylinder. Their heights are same and the diameter of the cone is equal to that of the cylinder.

What is the ratio of the volume of the cube to that of the cylinder ?

A) 4 : 3 B) 21 : 16
C) 14 : 11 D) 45 : 32
 
Answer & Explanation Answer: C) 14 : 11

Explanation:
The top view of the given assembly will look like the figure above
Outermost is the sphere. Inside that there is a cube and within that there is a cone and cylinder with same radius.
Here side of cube = a
Diameter of Sphere = body diagnol = √3 a
Radius of sphere = √3 a/2 =r1
Height of Cylinder = Height of cone = side of cube = a =h
Radius of cylinder = Radius of cone = side of cube/2 = a/2 =r2(as shown in the figure)
VcubeVcylinder = a3πr22h = 14/11
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Q:

A solid brass sphere of radius 2.1 dm is converted into a right circular cylindrical rod of length 7cm. The ratio of total surface areas of the rod to the sphere is

A) 3:1 B) 1:3
C) 7:3 D) 3:7
 
Answer & Explanation Answer: C) 7:3

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0 1363
Q:

Point A divides segment BC in the ratio 5:1. Co-ordinates of B are (6 ,-4) and C are (0,8). What are the co-ordinates of point A?

A) (-1 , 6) B) (1 , -6)
C) (-1 , -6) D) (1 , 6)
 
Answer & Explanation Answer: D) (1 , 6)

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0 1360
Q:

Find the curved surface area (in cm2) of a right circular cylinder of diameter 28 cm and height 12 cm.

A) 968 B) 924
C) 856 D) 1056
 
Answer & Explanation Answer: D) 1056

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Q:

The total surface area of a cuboid is 376 sq cm. Find its volume if its length and breadth are 10 cm and 8 cm respectively?

A) 960 cubic cms B) 240 cubic cms
C) 480 cubic cms D) 720 cubic cms
 
Answer & Explanation Answer: C) 480 cubic cms

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Q:

The total surface area of a hemisphere is 462 sq cm, what is its curved surface area? (Take π = 22/7)

A) 616 sq cms B) 154 sq cms
C) 308 sq cms D) 462 sq cms
 
Answer & Explanation Answer: C) 308 sq cms

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Q:

If PQ and PR be the two tangents to a circle with centre O such that ∠QPR = 120° then ∠POQ is

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

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0 1350
Q:

Two circles touch externally. The sum of their areas is 130π sq.cm and the distance between their centers is 14 cm. The radius of the bigger circle is

A) 22 cm B) 11 cm
C) 33 cm D) 44 cm
 
Answer & Explanation Answer: B) 11 cm

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