Question

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

Answer 1

The surface area of a sphere is
`A = 4 \pi r^(2)` and if the original S.A was is enlarged to have it 9 times greater, the radius would be multiplied by 3 or roughly 2.99626 rounded off to 3.0.

For example, let us assign values.
Let A=90

A= 90*9 = 810


`90 = 4 \pi r^(2)` and
`810 = 4 \pi r ^(2)`

the first r is 2.68 and the second r is 8.03

then,
`(8.03)/(2.68) = 2.99626` or rounded off to 3.