Answered



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.)

AFind the ratio of their surface areas.

BFind the ratio of their volumes.

Verified Answer :

The area of a sphere is defined by 4 pi r^2 

So if the radius of the first sphere is 2r, then it would be (2r)^2 = 4r^2 

The rest is the same. So the ratio of their surface areas would be 

4 pi 4r^2 divided by 
4 pi r^2 

or 4.

I hope my answer has come to your help. Thank you for posting your question here in Brainly. We hope to answer more of your questions and inquiries soon. Have a nice day ahead!

Answer:

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:

\(A = 4 \pi r^2\)

a.

Ratio of their surface areas:

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

\(A = 4 \pi r^2\)  and \(A' = 4 \pi r'^2\)

then;

\(A : A' =4 \pi r^2 : 6 \pi r'^2\)

⇒\(A : A' = r^2 : r'^2\)

⇒\(A : A' = (2r')^2 : r'^2\)

⇒\(A : A' = 4r'^2 : r'^2\)

⇒\(A : A' = 4: 1\)

b.

Find the ratio of their volumes.

Volume of sphere(V) is given by:

\(V = \frac{4}{3} \pi r^3\)

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

⇒\(V = \frac{4}{3} \pi r^3\) and \(V'= \frac{4}{3} \pi r'^3\)

then;

\(\frac{V}{V'} =\frac{\frac{4}{3} \pi r^3}{\frac{4}{3} \pi r'^3} = \frac{r^3}{r'^3}\)

⇒\(\frac{V}{V'} = \frac{(2r')^3}{r'^3}= \frac{8r'^3}{r'^3} = \frac{8}{1}\)

V : V' = 8: 1

Related Questions