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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 diameter of the driving wheel of a cart is 154 cm. Calculate the revolution per minute [RPM] of the wheel in order to keep a speed of 33 kmph?

A) 114 B) 112
C) 110 D) 108
 
Answer & Explanation Answer: A) 114

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0 710
Q:

The length of the diagonal and the breadth of a rectangle are 29 cm and 20 cm respectively. Find its perimeter (in cm).

 

A) 164 B) 82
C) 21 D) 42
 
Answer & Explanation Answer: B) 82

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0 710
Q:

Points P and Q lie on side AB and AC of triangle ABC respectively such that segment PQ is parallel to side BC. If the ratio of AP:PB is 1:4 and area of Δ APQ is 4 sq cm, what is the area of trapezium PQCB?

A) 60 sq cm B) 16 sq cm
C) 96 sq cm D) 21 sq cm
 
Answer & Explanation Answer: C) 96 sq cm

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0 708
Q:

The length and breadth of a rectangular piece of a land are in a ratio 5:3. The owner spent Rs. 6000 for surrounding it from all sides at Rs.7.50 per metre. The difference between its length and breadth is

A) 50 metres B) 100 metres
C) 150 metres D) 250 metres
 
Answer & Explanation Answer: B) 100 metres

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0 708
Q:

Two circles touch each other externally. The distance between their centres is 7 cm. If the radius of one circle is 4 cm, then the radius of the other circle will be

A) 3 cm B) 4 cm
C) 5.5 cm D) 3.5 cm
 
Answer & Explanation Answer: A) 3 cm

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0 707
Q:

Which of the following triangle is formed when the triangle has all the three medians of equal length?0

A) Scalene B) Isosceles
C) Equilateral D) Right angled
 
Answer & Explanation Answer: C) Equilateral

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0 706
Q:

Find the volume (in cm3) of a cuboid of length, breadth and height of 10.5 cm, 8 cm and 9 cm respectively.

A) 307 B) 541
C) 355 D) 756
 
Answer & Explanation Answer: D) 756

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0 703
Q:

Calculate the value of ∡OBC + ∡BAC, if O is the circum-center of the triangle ABC inscribed in the circle.

 

 

 

A) 60 deg B) 90 deg
C) 120 deg D) 130 deg
 
Answer & Explanation Answer: B) 90 deg

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0 700