Question

The radius of one sphere is twice as great as the radius of a second sphere. Find the ratio of their surface areas. 1/2 1/4 1/8 1/16

Answer 1

Surface area #1: 4*pi*r^2

Surface area #2: 4*pi*(2r)^2 This is 4 times larger than the previous surface area.

Answer 2

Option 2 -
`(1)/(4)`

Explanation:

Given : The radius of one sphere is twice as great as the radius of a second sphere.

To find : The ratio of their surface areas?

Solution :

The surface area of the sphere is
`A=4\pi r^2`

Let, the radius of one sphere is r

The surface area of one sphere is
`A_1=4\pi r^2`

Radius of second sphere is R

The surface area of second sphere is
`A_2=4\pi R^2`

According to question,

The radius of one sphere is twice as great as the radius of a second sphere.

i.e, r=2R

Now, The ratio of their surface areas is

`Ratio=(A_2)/(A_1)`

`Ratio=(4\pi R^2)/(4\pi r^2)`

Substitute r=2R,

`Ratio=\frac{4\pi R^2{4\pi (2R)^2}}`

`Ratio=(4\pi R^2)/(16\pi R^2)`

`Ratio=(1)/(4)`

Therefore, Option 2 is correct.

The ratio of their surface area is
`(1)/(4)`