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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 rectangular field is to be fenced on three sides leaving a side of 20 feet uncovered. If the area of the field is 680 sq. feet, how many feet of fencing will be required?

A) 34 B) 40
C) 68 D) 88
 
Answer & Explanation Answer: D) 88

Explanation:

We have: l = 20 ft and lb = 680 sq. ft.

So, b = 34 ft.

Length of fencing = (l + 2b) = (20 + 68) ft = 88 ft.

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2 4660
Q:

Which of the following option is CORRECT for SAS similarly criterion for the triangle ABC and DEF?

 

 

A) B)
C) D) All options are correct
 
Answer & Explanation Answer: D) All options are correct

Explanation:
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0 4550
Q:

A town has a population of 4000 requires 140 liters of water per head. It has a tank measuring 18m x 12m x 8m. The water of this tank will suffice for ____ days?

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

Explanation:

Water required = 4000 x 140 = 560000 lit = 560 cu.m (1 cu.m = 1000 lit)

Volume of tank = 18 x 12 x 8 = 1728 cu.m

Water of this tank will suffice for = 1728/560 = 3 days.

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Exam Prep: AIEEE , Bank Exams , CAT , GATE
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35 4527
Q:

The volume of a hemisphere is 2425.5 cm³. Find its diameter (in cm).

 

A) 10.5   B) 42
C) 21 D) 31.5
 
Answer & Explanation Answer: C) 21

Explanation:
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0 4491
Q:

The length of a rectangle is halved, while its breadth is tripled. What is the percentage change in area?

A) 25% increase B) 50% increase
C) 50% decrease D) 75% decrease
 
Answer & Explanation Answer: B) 50% increase

Explanation:

Let original length = x and original breadth = y.

Original area = xy.

 

New length = x/2 and New breadth = 3y.

New area = (x/2 * 3y) = (3/2 )xy

 

Therefore,  Increase % = [(1/2)xy * (1/xy) * 100] % = 50%

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0 4393
Q:

Two cylindrical buckets have their diameters in the ratio 3:1 and their heights are as 1: 3. Find the ratio of their volumes.

A) 2:1 B) 3:1
C) 4:1 D) 5:1
 
Answer & Explanation Answer: B) 3:1

Explanation:

v1v2=r12×h1r22×h2 

 

d1 = 2r1 and d2 = 2r2 are diameters

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2 4360
Q:

A cistern 6m long and 4 m wide contains water up to a depth of 1 m 25 cm. The total area of the wet surface is:

A) 49 sq.m B) 50 sq.m
C) 51 sq.m D) 52 sq.m
 
Answer & Explanation Answer: A) 49 sq.m

Explanation:

ke

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0 4220
Q:

A large cube is formed from the material obtained by melting three smaller cubes of 3,4 and 5 cm side. What is the ratio of the total surface areas of the smaller cubes and the large cube?

A) 2 : 1 B) 3 : 2
C) 25 : 18 D) 27 : 20
 
Answer & Explanation Answer: C) 25 : 18

Explanation:

ke

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