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:

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

 A) 36 B) 232 C) 216 D) 484

Explanation:

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

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

93 32115
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

Explanation:

Let the edge of the cube bea. Then,

6$a2$ = 1734

=> a = 17 cm.

Volume =  $a3$ = $173$ = 4193 cu.cm

56 28537
Q:

Consider the following two triangles as shown in the figure below.

Choose the correct statement for the above situation.

 A) 1 B) 2 C) 3 D) 4

Explanation:

Filed Under: Volume and Surface Area
Exam Prep: Bank Exams

0 28009
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

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

41 24816
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

Explanation:

Let the breadth of the wall be x metres.

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

x * 5x * 40x = 12.8

=>

=> x = 4/10 m

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

52 23910
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

Explanation:

35 22573
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

Explanation:

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

35 22112
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

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