The radius of one sphere is twice as great as the radius of a second sphere.
(note: write the ratios as a comparison of the smaller to the larger.)
a. find the ratio of their surface areas.
b. find the ratio of their volumes.

Let radius of one sphere be r and radius of second sphere be r'.

As per the statement

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

⇒r = 2r'

We have to find the ratio of their surface areas.

Surface area of sphere(A) is given by:

a.

Ratio of their surface areas:

Let A be the surface area of one sphere and A' be the surface area of second sphere.

 and

then;

⇒

⇒

⇒

⇒

b.

Find the ratio of their volumes.

Volume of sphere(V) is given by:

Let V be the Volume of one sphere and V' be the Volume of second sphere.

⇒ and

then;

⇒

V : V' = 8: 1

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step-by-step explanation: