Question

The radius of a sphere is increased by 10%. prove that the volume will be increased by 33.1% approximately​

Answer 1

Answer:

The volume of a sphere = 4/3 πr3 10% increase in radius = 10% r Increased radius = r + 1/10 r = 11/10 r The volume of the sphere now becomes Read more on Sarthaks.com - https://www.sarthaks.com/876219/the-radius-sphere-is-increased-by-10-prove-that-the-volume-will-increased-approximately?show=876221#a876221

Answer 2

➵ Let Radius of Sphere = r

$Volume= \frac{4}{3} \pi {r}^{3}$

$Radius \: is \: increased \: by \: 10\% = r + \frac{10}{100}r$

$\: \: \: = r + \frac{r}{10} = \frac{11r}{10}$

$volume \: = \frac{4}{3} \pi \times \frac{ {11}^{3} }{ {1000}^{r3} }$

$\: \: increased \: value\% =$

$\frac{ (\frac{1331}{1000} - 1) \frac{4}{3}\pi {r}^{3} }{ \frac{4}{3} \pi {r}^{3} } \times 100$

$\: \: = \frac{331}{1000} \times 100 = 33.1\%$

∴ Volume Increased by 33.1