Q5 of 168 Page 216

Find the approximate change in the surface area of a cube of side x metres caused by decreasing the side by 1%.

It is given that the surface area of cube (S) of a side x

⇒ S = 6x²

= (12x)Δx

= (12x)(0.01x)

= 0.12x²

Therefore, the approximate change in the surface area of a cube of side x metres caused by decreasing the side by 1% is 0.12x².

Find the approximate value of f (5.001), where f (x) = x³ – 7x2 + 15.

Find the approximate change in the volume V of a cube of side x metres caused by increasing the side by 1%.

If the radius of a sphere is measured as 7 m with an error of 0.02 m, then find the approximate error in calculating its volume.

If the radius of a sphere is measured as 9 m with an error of 0.03 m, then find the approximate error in calculating its surface area.