Let the initial radiuS of sphEre be X initial vOlm of sphere= 4/3πr^2neW radiuS oF sphere, r' = r+10% if r= 11r/10neW vOlm of sphere= 4/3π(11/10)^3 % inCrease in vOlm = increase in volume/ initial volume × 100=: {4/3π(11r/10} - (4/3πr^3) //4/3πr^3 × 100 =: (1331/1000 - 1) × 100=: 331/10=: 33.1 hE'nCe, the volume is inCrease bY 33.1 % cheer prOved hurrahhhhhhhhhhhhhhh

Explanation:

To find the percentage increase in volume when the radius of a sphere is increased by 10%, we need to understand the relationship between the radius of a sphere and its volume.

Volume of a Sphere:
The volume of a sphere is given by the formula:
V = (4/3) * π * r^3
where V is the volume and r is the radius of the sphere.

Percentage Increase:
To find the percentage increase, we need to calculate the difference between the new volume and the original volume, and then express it as a percentage of the original volume.

Step 1: Calculate the original volume:
Let's assume the original radius of the sphere is 'r'.
The original volume of the sphere is:
V1 = (4/3) * π * r^3

Step 2: Calculate the new volume:
If the radius of the sphere is increased by 10%, the new radius becomes:
New radius = r + (10/100) * r
New radius = r + 0.1r
New radius = 1.1r

The new volume of the sphere is:
V2 = (4/3) * π * (1.1r)^3

Step 3: Calculate the difference between the new and original volumes:
Difference = V2 - V1

Step 4: Calculate the percentage increase:
Percentage Increase = (Difference / V1) * 100

Final Calculation:
Let's substitute the values and calculate the percentage increase.

V1 = (4/3) * π * r^3
V2 = (4/3) * π * (1.1r)^3

Difference = V2 - V1
Percentage Increase = (Difference / V1) * 100

Conclusion:
The percentage increase in volume when the radius of a sphere is increased by 10% can be calculated using the formula mentioned above.