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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 difference between the length and breadth of a rectangle is 23 m. If its perimeter is 206 m, then its area is:

A) 1520 sq.m B) 2420 sq.m
C) 2480 sq.m D) 2520 sq.m
 
Answer & Explanation Answer: D) 2520 sq.m

Explanation:

We have: (l - b) = 23 and 2(l + b) = 206 or (l + b) = 103. 

Solving the two equations, we get: l = 63 and b = 40. 

Area = (l x b) = (63 x 40) sq.m

= 2520 sq.m

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1 4900
Q:

A Conical tent was erected by the army at a base camp with height 3 m and base diameter 10 m. If every person requires 3.92 cu.m air, then how many persons can be seated in that tent approximately?

A) 20 B) 19
C) 17 D) 22
 
Answer & Explanation Answer: A) 20

Explanation:

Given height of the conical tent = 3 m

Diameter = 10 => Radius = D/2 = 10/2 = 5 m 

Now, as the tent is in the conical form

Volume of the conical tent = πr2h3 

=> (22 x 5 x 5 x 3) / (7 x 3) 

= 22 x 25/7 

= 78.54 cu.m 

Given each person requires 3.92 cu.m of air 

=> Number of persons can be seated in the tent = 78.54/3.92 = 20.03 =~ 20

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17 4844
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 4682
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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35 4564
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 4416
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 4408
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 4254
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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