Question

How does the total surface area of a box change if
i) Each dimension is doubled
ii) Each dimension is tripled

Answer 1

: Let the length of the edge of the cube be 'x' cm (i) Total surface area = 6x2 cm2 Increased length of the edge = 2x Total surface area = 6(2x)2 cm2 = 24x2 cm2 If the edge of the cube is doubled surface area of the cube increases by 4 times. (ii) Volume of the cube = x3 cm3 Increased length of the edge = 2x Volume of the cube formed = (2x)3 cm3 = 8x3 cm3 If the edge of the cube is doubled volume of the cube is increases by 8 times.

Answer 2

SOLUTION

A box is in the form of a cuboid

Previous dimensions- length(l) , breadth(b) , height (h)

I)

CASE 1 - Dimensions are doubled

The new dimensions will be

2l, 2b, 2h

TSA of a cuboid is given by - 2(lb+bh+hl)

Substituting the new dimensions, we get

TSA - 2(2l×2b + 2b×2h + 2h×2l)

TSA- 2(4lb + 4bh + 4hl)

TSA - 4 (2(lb + bh + hl)

Hence, The total surface area becomes four times that of the original

II) CASE 2 - Dimensions are tripled

New dimensions are

3l, 3b, 3h

Using the TSA formula, we get

TSA - 2(3l×3b + 3b×3h +3h×3l)

TSA - 2(9lb + 9bh + 9hl)

TSA - 9 (2(lb + bh + hl)

Hence the TSA becomes 9 times that of the original