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 Volume and Surface Area Questions

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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:

How many cubes of 3cm edge can be cut out of a cube of 18cm edge

A) 36 B) 232
C) 216 D) 484
 
Answer & Explanation Answer: C) 216

Explanation:

number of cubes=(18 x 18 x 18) / (3 x 3 x 3) = 216

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93 31738
Q:

The surface area of a cube is 1734 sq. cm. Find its volume

A) 2334 cubic.cm B) 3356 cubic.cm
C) 4913 cubic.cm D) 3478 cubic.cm
 
Answer & Explanation Answer: C) 4913 cubic.cm

Explanation:

Let the edge of the cube bea. Then, 

 6a2 = 1734 

 => a = 17 cm.

  Volume =  a3 = 173 = 4193 cu.cm

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56 28001
Q:

Three solid cubes of sides 1 cm, 6 cm and 8 cm are melted to form a new cube. Find the surface area of the cube so formed

A) 486 B) 586
C) 686 D) 786
 
Answer & Explanation Answer: A) 486

Explanation:

Volume of new cube =  13+63+83cm3= 729cm3  

Edge of new cube = 7293 = 9cm

Surface area of the new cube = ( 6 x 9 x 9) sq.cm = 486 sq.cm

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41 24412
Q:

The volume of a wall, 5 times as high as it is broad and 8 times as long as it is high, is 12.8 cu. meters. Find the breadth of the wall.

A) 40cm B) 30cm
C) 20cm D) 10cm
 
Answer & Explanation Answer: A) 40cm

Explanation:

Let the breadth of the wall be x metres. 

Then, Height = 5x metres and Length = 40x metres.  

x * 5x * 40x = 12.8   

=>x3 =12.8/200 = 128/2000 =64/1000  

=> x = 4/10 m  

=> x = (4/10)*100 = 40 cm

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52 23334
Q:

A cistern of capacity 8000 litres measures externally 3.3 m by 2.6 m by 1.1 m and its walls are 5 cm thick. The thickness of the bottom is:

A) 90 cm B) 1 dm
C) 1 m D) 1.1 cm
 
Answer & Explanation Answer: B) 1 dm

Explanation:

ke

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35 22115
Q:

Find the length of the longest pole that can be placed in a room 12 m long 8m broad and 9m high.

A) 14m B) 15m
C) 16m D) 17m
 
Answer & Explanation Answer: D) 17m

Explanation:

Length of longest pole = Length of the diagonal of the room

 

122+82+92=289 = 17m

 

 

 

 

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35 21832
Q:

Find the number of bricks, each measuring 24 cm x 12 cm x 8 cm, required to construct a wall 24 m long, 8m high and 60 cm thick, if 10% of the wall is filled with mortar?

A) 35000 B) 45000
C) 55000 D) 65000
 
Answer & Explanation Answer: B) 45000

Explanation:

Volume of the wall = (2400 x 800 x 60)  cu.cm  

 

Volume of bricks   = 90% of the volume of the wall 

= [(90/100) x 2400 x 800 x 60] cu.cm  

 

Volume of 1 brick = (24 x 12 x 8)  cu.cm 

 

Number of bricks = [(90/100) x (2400 x 800 x 60) ]/ (24 x 12 x 8) = 45000

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18 20407
Q:

The dimensions of an open box are 50 cm, 40 cm and 23 cm. Its thickness is 2 cm. If 1 cubic cm of metal used in the box weighs 0.5 gms, find the weight of the box.

A) 8.04kg B) 8.14kg
C) 8.24kg D) 9.04kg
 
Answer & Explanation Answer: A) 8.04kg

Explanation:

Volume of the metal used in the box = External Volume - Internal Volume 

                                                    = [(50 x 40 x 23) - (44 x 34 x 20)] cu.cm  

                                                    = 16080 cu.cm 

 

Weight of the metal =[(16080 x 0.5)/1000] kg = 8.04 kg.

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46 18869