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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:

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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Q:

In the given figure, ABCD is a square, BCXYZ is a regular pentagon and ABE is an  equilateral triangle. What is the value in deg of EBZ?

A) 102 B) 98
C) 78 D) 64
 
Answer & Explanation Answer: A) 102

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0 1399
Q:

A cone of radius 7 cm and height 12 cm is completely filled with water. This water is emptied into an empty cylindrical vessel of radius 3.5 cm. What will be the height of water in this vessel?

A) 16 cm B) 32 cm
C) 5.33 cm D) 8 cm
 
Answer & Explanation Answer: A) 16 cm

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0 1399
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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Q:

The area of a semicircle is 1925 sq.cm. Calculate its perimeter (in cm).

A) 360 B) 80
C) 160 D) 180
 
Answer & Explanation Answer: D) 180

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2 1397
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 1395
Q:

The base of a prism is in the shape of an equilateral triangle. If the perimeter of the base is 18 cm and the height of the prism is 20 cm, then what is the volume (in cm3) of the prism?

A) 60√3 B) 30√6
C) 60√2 D) not know
 
Answer & Explanation Answer: D) not know

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0 1394
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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