Question

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

Answer 1

let the radius be 100 after increasing it will be 110 now using volume formula for sphere it will increase approx 33.1%

Answer 2

The volume will be increased by 33.1% approximately

Solution:

The volume of sphere is given as:

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

Where, "r" is the radius of sphere

The radius of a sphere is increased by 10%

Now,

$Radius = \frac{110}{100} \times r = \frac{11}{10}r$

Now, new volume is:

$v = \frac{4}{3} \pi \times (\frac{11}{10}r)^3\\\\v = \frac{4}{3} \pi \times r^3 \times \frac{1331}{1000}$

Now, volume increased is given as:

$\frac{\frac{4}{3} \pi \times r^3 \times \frac{1331}{1000} - \frac{4}{3} \times \pi r^3 }{\frac{4}{3} \times \pi r^3 } \times 100 \% \\\\(\frac{1331}{1000} - 1) \times 100 \% \\\\0.331 \times 100 \%\\\\\33.1 \%$

Thus, the volume will be increased by 33.1% approximately

Learn more:

If the radius of the sphere is increased by 100%, the volume of the corresponding sphere is increased by (a) 200% (b) 500% (c) 700% (d) 800%

https://brainly.in/question/14179535

If the radius of a sphere is increased by 2 cm, then its surface area increases by 352 cm^2 . The radius of the sphere before the increase was:

https://brainly.in/question/8184272