Question

If each side of a cube is halved, how much % will its surface area changed?​

Answer 1

Answer:

75%

Step-by-step explanation:

Let the side of cube be

$a$

Surface area of cube

$= 6 {a}^{2}$

New side of cube

$= \frac{a}{2}$

New surface area

$= 6 {( \frac{a}{2} )}^{2}$

$= \frac{6}{4} {a}^{2}$

$= \frac{3}{2} {a}^{2}$

Change in surface area

$= 6 {a}^{2} - \frac{3}{2} {a}^{2}$

$= \frac{9}{2} {a}^{2}$

% change

$= \frac{ \frac{9}{2} {a}^{2} }{6 {a}^{2} } \times 100$

$= \frac{3}{4} \times 100$

$= 75\%$