Volume of sphere = 4/3πr^{3}
∵ Radius = r = 10 cm
∴ Volume of sphere = 4/3π × 10 × 10 × 10
= 4000π/3 cm^{3}
Now, increase the radius 5%
Radius of new sphere = (10 × 105)/100
= 21/2 cm
Volume of new sphere = 4/3π × 21/2 × 21/2 × 21/2
= 9261π/6 cm^{3}
Increase volume = Volume of new sphere – Volume of sphere
= 9261π/6 - 4000π/3
= (9261π - 8000π)/6
= 1261π/6 cm
Percentage of increasing volume = (1261π/6 × 100)/(4000π/3)
= (1261π × 100 × 3)/(4000π × 6) = 1261/80%
= 15 61/80%