Question

How does the total surface area of a box change if
(i) Each dimension is doubled?
(ii) Each dimension is tripled?
Express in words. Can you find the area if each dimension is raised to n times?

Answer 1

(i) If each dimension is doubled then the total surface area becomes, = 2((4lb) + (4bh) + (4lh))
= 4 × [2(lb + bh + lh)]
∴ the area becomes four times.

(ii) If each dimension is tripled then the total surface area becomes, = 2((9lb) + (9bh) + (9lh))
= 9 × [2(lb + bh + lh)]
∴ the area becomes nine times.
It is clear from the above two solutions that the area of cuboid becomes n2times the previous area if each dimension raised to n times.