# Volume and Surface Areas Questions

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%

58 12519
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.

14 4163
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

32 3996
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

=>$\inline&space;\fn_jvn&space;x^3=\frac{12.8}{200}=\frac{128}{2000}=\frac{64}{1000}$

=>$\inline&space;\fn_jvn&space;x=\frac{4}{10}m$

=>$\inline&space;\fn_jvn&space;x=\frac{4}{10}\times&space;100=40cm$

10 3285
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 B) 50 C) 53.5 D) 55

Explanation:

Area of the wet surface = [2(lb + bh + lh) - lb]

= 2(bh + lh) + lb

= [2 (4 x 1.25 + 6 x 1.25) + 6 x 4]$\inline \fn_jvn m^{2}$

= 49$\inline \fn_jvn m^{2}$