Question 59

If each edge of a cube is increased by 50%, the percentage increase in its surface area is

Solution

Let edge of cube, $$a = 10$$ cm

Surface Area, $$S = 6 a^2 = 6 (10)^2 = 600 cm^2$$

When edge is increased by 50%

=> New edge of cube, $$a' = 10 + \frac{50}{100} \times 10 = 15$$ cm

New surface area, $$S' = 6 (a')^2 = 6 (15)^2 = 1350 cm^2$$

$$\therefore$$ % increase in surface area = $$\frac{1350 - 600}{600} \times 100$$

= $$\frac{750}{6} = 125 \%$$

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