The surface area of a sphere is given by the formula 4πr², where r is the radius of the sphere.

If the surface area is enlarged 9 times, then the new surface area is 9 * 4πr² = 36πr².

However, this is also the surface area of a sphere with a larger radius. Let's call this larger radius R. So we have 36πr² = 4πR².

Dividing both sides by 4π, we get 9r² = R².

Taking the square root of both sides, we get R = 3r.

So, the original radius is multiplied by 3.

Question

The surface area of a sphere is given by the formula 4πr², where r is the radius of the sphere.

If the surface area is enlarged 9 times, then the new surface area is 9 * 4πr² = 36πr².

However, this is also the surface area of a sphere with a larger radius. Let's call this larger radius R. So we have 36πr² = 4πR².

Dividing both sides by 4π, we get 9r² = R².

Taking the square root of both sides, we get R = 3r.

So, the original radius is multiplied by 3.

Knowee AI · Accepted Answer

The surface area of a sphere is given by the formula 4πr², where r is the radius of the sphere.

If the surface area is enlarged 9 times, then the new surface area is 9 * 4πr² = 36πr².

However, this is also the surface area of a sphere with a larger radius. Let's call this larger radius R. So we have 36πr² = 4πR².

Dividing both sides by 4π, we get 9r² = R².

Taking the square root of both sides, we get R = 3r.

So, the original radius is multiplied by 3.

If a spherical ball is enlarged so that its surface area is 9 times greater than its original surface area, then the original radius is multiplied by ____.