Question

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%

Answer 1

Answer: (c) 700% is the correct option

Step-by-step explanation: if you're solving this for NTSE or objective type then assume r as 1, then R=r+100% of r i.e. 2r so the ratio of volume comes out to be 8:1 and therefore the increase is 8-1=7 .... Which is 700% of 1

Answer 2

The volume of the corresponding sphere is increased by 700%

Step-by-step explanation:

Let radius of sphere=r

After increasing 100%,  radius of  sphere=r+100% of r=$r+\frac{100}{100}\times r$

Radius  of sphere=$r+r=2r$

Volume of sphere,V=$\frac{4}{3}\pi r^3$

Initial volume of sphere=$\frac{4}{3}\pi r^3$

Where

r= Radius of sphere

Substitute radius =2r

Now, volume of sphere=$\frac{4}{3}\pi (2r)^3=\frac{4}{3}\pi (8r^3)$

Increase value of volume=$\frac{4}{3}\pi (8r^3)$-\frac{4}{3}\pi r^3[\tex]

Increase value of volume=$\frac{4}{3}\pi r^2\cdot 7$

Percentage of increase in volume =$\frac{increase\;value\;in volume}{original\;volume}\times 100=\frac{\frac{4}{3}\pi r^3\cdot 7}{\frac{4}{3}\pi r^3}\times 100$=700%

Hence, option c is true.

c) 700%

# Learns more:

https://brainly.in/question/85630: Answered by Kidrah