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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 curved surface area of a cylinder is 616 sq cm and height is 14 cm, find its radius?

A) 14 cm B) 7 cm
C) 21 cm D) 3.5 cm
 
Answer & Explanation Answer: B) 7 cm

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0 1258
Q:

In ΔPQR, PS and PT are bisectors of ∠QPR and ∠QPS respectively. If ∠QPT = 30°, PT = 9 cm and TR = 15 cm, then what is the area (in cm2) of ΔPTR

A) 36 B) 54
C) 72 D) 216
 
Answer & Explanation Answer: B) 54

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0 1256
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 1254
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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0 1253
Q:

In triangle ABC, ∠ABC = 15 deg. D is a point on BC such that AD = BD. What is the measure of ∠ADC (in degrees)?

A) 15 B) 30
C) 45 D) 60
 
Answer & Explanation Answer: B) 30

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1 1251
Q:

The length of the common chord of two intersecting circles is 12 cm. If the diameters of the circles are 15 cm and 13 cm, then what is the distance (in cm) between their centers?

A) 7/2 B) 7
C) 7√2 D) 14
 
Answer & Explanation Answer: B) 7

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1 1248
Q:

­ A wooden bowl is in shape of a hollow hemisphere of internal radius 8 cm and thickness 1 cm. Find the total surface area of the bowl?

A) 964.85 sq cms B) 1125.14 sq cms
C) 1687.71 sq cms D) 281.29 sq cms
 
Answer & Explanation Answer: A) 964.85 sq cms

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1 1246
Q:

ABCD is a quadrilateral with AB = 9 cm, BC = 40 cm, CD = 28 cm, DA = 15 cm and angle ABC is a right –angel. 
What is the area of triangle ADC?

A) 126 SQ.CM B) 124 SQ.CM
C) 122 SQ.CM   D) 120 SQ.CM
 
Answer & Explanation Answer: A) 126 SQ.CM

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