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:

700 percent pls see the answer in the pic attached

Answer 2

(c) 700%

The volume of the corresponding sphere is increased by 700% .

Explanation:

We know that the volume of sphere is given by :-

$V=\dfrac{4}{3}\pi r^3$, where  r = radius of sphere.

If the radius is increased by 100 % , then the new radius will be

R = r+100% of r = r+r= 2r

New Volume =$V_1=\dfrac{4}{3}\pi (2r)^3=\dfrac{4}{3}\pi (8)(r)^3$

$\Rightarrow\ V_1=8(\dfrac{4}{3}\pi r^3)=8V$

Percentage of increase in volume =$\dfrac{V_1-V}{V}\times100$

$=\dfrac{8V-V}{V}\times100\\\\=\dfrac{7V}{V}\times100=7\times100=700%$

Hence, the volume of the corresponding sphere is increased by 700% .

Therefore , the correct answer is (c) 700%  .

# Learn more :

Radius of a circle is increased by 200%, then its area will be increased by:

7. If the radius of ac

(B) 200%

(C) 400%

(D) 800%

(A) 100%​

https://brainly.in/question/14448135