Q5 of 20 Page 219

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?

(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.


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