# Volume and Surface Areas 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 = 2(lb +bh +lh) sq.units

3. Diagonal =$\sqrt{3}a$ units

III. CYLINDER

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

1.Volume = $\inline (\prod r^{2}h)$ cubic units

2. Curved surface area = $\inline (2\prod rh )$ sq.units

3. Total surface area = $\inline (2\prod rh+2\prod r^{2} )$ sq.units

IV. CONE

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

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

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

3. Curved surface area = $\inline \left (\prod rl )$ sq.units

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

V. SPHERE

Let the radius of the sphere be r. Then,

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

2. Surface area = $\inline \left (4\prod r^{2})$ sq.units

VI. HEMISPHERE

Let the radius of a hemisphere be r. Then,

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

2. Curved surface area = $\inline \left ( 2\prod r^{2} )$ sq.units

3. Total surface area = $\inline \left ( 3\prod r^{2} )$ sq.units

Q:

If each edge of a cube is increased by 50%, find the percentage increase in Its surface area

 A) 125% B) 150% C) 175% D) 110%

Explanation:

Let the edge = a cm

So increase by 50 % = $\inline \fn_jvn a+\frac{a}{2}$ = $\inline \fn_jvn \frac{3a}{2}$

Total surface Area of original cube = $\inline \fn_jvn 6a^{2}$

TSA of new cube = $\inline \fn_jvn 6(\frac{3a}{2})^{2}$

=$\inline \fn_jvn 6\times \frac{9a^2}{4}$=  $\inline \fn_jvn 13.5a^{2}$

Increase in area = $\inline \fn_jvn 13.5a^{2} -6a^{2}$ =$\inline \fn_jvn 7.5a^{2}$

$\inline \fn_jvn 7.5a^{2}$ Increase % =$\inline \fn_jvn \frac{7.5a^{2}}{6a^2}\times 100$ = 125%

156 32872
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

49 12024
Q:

A rectangular block 6 cm by 12 cm by 15 cm is cut up into an exact number of equal cubes. Find the least possible number of cubes.

 A) 30 B) 40 C) 10 D) 20

Explanation:

Volume of the block = (6 x 12 x 15) $\inline&space;\fn_jvn&space;cm^3$ = 1080 $\inline&space;\fn_jvn&space;cm^3$

Side of the largest cube = H.C.F. of 6 cm, 12 cm, 15 cm

= 3 cm.

Volume of this cube  = (3 x 3 x 3) $\inline&space;\fn_jvn&space;cm^3$ = 27 $\inline&space;\fn_jvn&space;cm^3$

Number of cubes =$\inline \left ( \frac{1080}{27} \right )$ = 40.

27 10399
Q:

A hall is 15 m long and 12 m broad. If the sum of the areas of the floor and the ceiling is equal to the sum of the areas of four walls, the volume of the hall is:

 A) 720 B) 900 C) 1200 D) 1800

Explanation:

22 8339
Q:

A right triangle with sides 3 cm, 4 cm and 5 cm is rotated the side of 3 cm to form a cone. The volume of the cone so formed is:

 A) 12 pi cub.cm B) 15 pi cub.cm C) 16 pi cub.cm D) 20 pi cub.cm