# 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%

133 26824
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

47 10147
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.

24 8123
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 =  $\inline \fn_jvn \left ( 1^{3}+6^{3}+8^{3} \right )cm^{3}$$\inline \fn_jvn 729cm^{3}$

Edge of new cube = $\inline \fn_jvn \sqrt[3]{729}$ = 9cm

$\inline \fn_jvn \therefore$ Surface area of the new cube = ( 6 x 9 x 9) $\inline \fn_jvn cm^{2}$ = 486 $\inline \fn_jvn cm^{2}$

13 6209
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