# Volume and Surface Area Questions

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 =$\sqrt{{l}^{2}+{b}^{2}+{h}^{2}}$ units

II. CUBE

Let each edge of a cube be of length a. Then,

1. Volume = ${a}^{3}$ cubic units.

2. Surface area = $6{a}^{2}$ sq.units

3. Diagonal = $\sqrt{3}a$ units

III. CYLINDER

Let radius of base = r and Height (or Length) = h. Then,

1.Volume = $\left({\mathrm{\pi r}}^{2}\mathrm{h}\right)$ cubic units

2. Curved surface area = $\left(2\mathrm{\pi }rh\right)$ sq.units

3. Total surface area = $\left(2\mathrm{\pi rh}+2{\mathrm{\pi r}}^{2}\right)$ sq.units

IV. CONE

Let radius of base =r and Height = h. Then,

1. Slant height, $l=\sqrt{{h}^{2}+{r}^{2}}$ units

2. Volume = $\left(\frac{1}{3}{\mathrm{\pi r}}^{2}\mathrm{h}\right)$ cubic units.

3. Curved surface area = $\left(\mathrm{\pi rl}\right)$sq.units

4. Total surface area = $\left(\mathrm{\pi rl}+{\mathrm{\pi r}}^{2}\right)$sq.units

V. SPHERE

Let the radius of the sphere be r. Then,

1. Volume =$\left(\frac{4}{3}{\mathrm{\pi r}}^{3}\right)$ cubic units

2. Surface area = $\left(4{\mathrm{\pi r}}^{2}\right)$ sq.units

VI. HEMISPHERE

Let the radius of a hemisphere be r. Then,

1. Volume = $\left(\frac{2}{3}{\mathrm{\pi r}}^{3}\right)$ cubic units.

2. Curved surface area = $\left(2{\mathrm{\pi r}}^{2}\right)$ sq.units

3. Total surface area = $\left(3{\mathrm{\pi r}}^{2}\right)$ sq.units

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

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.

46 19598
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

Explanation:

Volume of the large cube = $33+43+53$ = 216 cu.cm.

Let the edge of the large cube be a.

So, $a3$= 216

=>a = 6 cm.

Required ratio = $632+42+52662=2518$

18 19136
Q:

The size of the wooden block is 5 x 10 x 20 cm .How many such blocks will be required to construct a solid wooden cube of minimum size?

 A) 6 B) 8 C) 12 D) 16

Explanation:

Side of smallest cube = L.C.M of 5, 10, 20 = 20cm

Volume of the cube = (20 x 20 x 20)cu.cm = 8000 cu.cm

Volume of the block= (5 x 10 x 20)cu.cm = 1000 cu.cm

Number of blocks = (8000/1000) = 8

Filed Under: Volume and Surface Area
Exam Prep: Bank Exams
Job Role: Bank PO

35 17213
Q:

A hollow iron pipe is 21 cm long and its external diameter is 8 cm. If the thickness of the pipe is 1 cm and iron weighs 8g/cu.cm, then the weight of the pipe is

 A) 3.6 kg B) 3.696 kg C) 36 kg D) 36.9 kg

Explanation:

Volume of iron = $227×42-32×21cm3$$462cm3$

Weight of iron = (462 x 8)gm = 3696 gm = 3.696 kg

28 16990
Q:

How many bricks, each measuring 25 cm x 11.25 cm x 6 cm, will be needed to build a wall of 8 m x 6 m x 22.5 cm?

 A) 5600 B) 6000 C) 6400 D) 7200

Explanation:

Number of bricks = volume of the wall/volume of one brick

= (800 x 600 x 22.5)/(25 x 11.25 x 6 )= 6400

20 16326
Q:

How many cubes of 10cm edge can be put in a cubical box of 1m edge

 A) 10 B) 100 C) 1000 D) 10000

Explanation:

Number of cubes= (100x100x100) / (10x10x10)= 1000

Filed Under: Volume and Surface Area
Exam Prep: Bank Exams
Job Role: Bank PO

45 16023
Q:

A cuboidal block 6cm x 9cm x 12cm is cut up into an exact number of equal cubes.The least possible number of equal cubes will be

 A) 6 B) 9 C) 24 D) 30

Explanation:

Volume of block=(6 x 9 x 12) cu.cm = 648 cu.cm

Side of largest cube = H.C.F of 6,9,12 = 3cm

Volume of the cube=(3 x 3 x 3)=27cu.cm

Number of cubes=(648/27)=24

Filed Under: Volume and Surface Area
Exam Prep: Bank Exams
Job Role: Bank PO

18 16003
Q:

If the volume of the cube is 729 $cm3$, then the surface area of the cube will be

 A) 486 sq.cm B) 456 sq.cm C) 446 sq.cm D) 476 sq.cm

Explanation:

volume = $a3$ = 729;

=> a = 9

surface area= 6$a2$ =  (6 x 9 x 9) = 486 sq.cm