Sure, let's solve this step by step.

1. The volume of a sphere is given by the formula V = 4/3 * π * r³, where r is the radius of the sphere.

2. If the radius increases by 200%, it means the new radius is 300% of the original, or 3 times the original radius.

3. So, the new volume V' = 4/3 * π * (3r)³ = 4/3 * π * 27r³ = 27 * V.

4. The percentage increase in volume is therefore (V' - V) / V * 100% = (27V - V) / V * 100% = 26 * 100% = 2600%.

So, the volume of the sphere increases by 2600% if its radius increases by 200%.

Question

Sure, let's solve this step by step.

1. The volume of a sphere is given by the formula V = 4/3 * π * r³, where r is the radius of the sphere.

2. If the radius increases by 200%, it means the new radius is 300% of the original, or 3 times the original radius.

3. So, the new volume V' = 4/3 * π * (3r)³ = 4/3 * π * 27r³ = 27 * V.

4. The percentage increase in volume is therefore (V' - V) / V * 100% = (27V - V) / V * 100% = 26 * 100% = 2600%.

So, the volume of the sphere increases by 2600% if its radius increases by 200%.

Knowee AI · Accepted Answer

Sure, let's solve this step by step.

1. The volume of a sphere is given by the formula V = 4/3 * π * r³, where r is the radius of the sphere.

2. If the radius increases by 200%, it means the new radius is 300% of the original, or 3 times the original radius.

3. So, the new volume V' = 4/3 * π * (3r)³ = 4/3 * π * 27r³ = 27 * V.

4. The percentage increase in volume is therefore (V' - V) / V * 100% = (27V - V) / V * 100% = 26 * 100% = 2600%.

So, the volume of the sphere increases by 2600% if its radius increases by 200%.

Find the percentage increase in the volume of a sphere, if its radius increases by 200%.