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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:

If ΔABC is an equilateral triangle of side 16 cm, then the length of altitude is

A) 2√3 cm B)  4√3 cm
C) 8√3 cm D)  5√3 cm
 
Answer & Explanation Answer: C) 8√3 cm

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2 1083
Q:

The radius of the circle circumscribing the three vertices of an equilateral triangle is 12 cm. Determine the height (in cm) of the equilateral triangle

A) 12 B) 14
C) 18 D) 20
 
Answer & Explanation Answer: C) 18

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4 1080
Q:

In triangle ABC, AD, BE and CF are the medians intersecting at point G and area of triangle ABC is 156 sq.cm. What is the area (in sq.cm) of triangle FGE?

A) 13 B) 26
C) 39 D) 52
 
Answer & Explanation Answer: A) 13

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0 1074
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 1073
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 sphere to that of cone?

A) 6√3:1 B) 7 : 2
C) 3√3:1   D) 5√3:1
 
Answer & Explanation Answer: A) 6√3:1

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)
Volume of sphere/volume of cone = 43πr1313πr22h = 6√3:1
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0 1067
Q:

PQ and RS are common tangents to two circles intersecting at A and B. AB, when produced both sides, meet the tangents PQ and RS at X and Y, respectively. If AB = 3 cm, XY = 5 cm, then PQ (in cm) will be

A) 3 cm B) 4 cm
C) 5 cm D) 2 cm
 
Answer & Explanation Answer: B) 4 cm

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0 1066
Q:

Diameter of wheel of a cycle is 21 cm. The cyclist takes 45 minutes to reach a destination at a speed of 16.5 km/hr. How many revolutions will the wheel make during the journey?

A) 12325 B) 18750
C) 21000 D) 24350
 
Answer & Explanation Answer: B) 18750

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0 1065
Q:

In ΔABC, ∠BAC = 90° and AD is drawn perpendicular to BC. If BD = 7 cm and CD = 28 cm, then what is the length (in cm) of AD?

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

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0 1059