Respuesta :
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.
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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:
[tex]A = 4 \pi r^2[/tex]
a.
Ratio of their surface areas:
Let A be the surface area of one sphere and A' be the surface area of second sphere.
[tex]A = 4 \pi r^2[/tex] and [tex]A' = 4 \pi r'^2[/tex]
then;
[tex]A : A' =4 \pi r^2 : 6 \pi r'^2[/tex]
⇒[tex]A : A' = r^2 : r'^2[/tex]
⇒[tex]A : A' = (2r')^2 : r'^2[/tex]
⇒[tex]A : A' = 4r'^2 : r'^2[/tex]
⇒[tex]A : A' = 4: 1[/tex]
b.
Find the ratio of their volumes.
Volume of sphere(V) is given by:
[tex]V = \frac{4}{3} \pi r^3[/tex]
Let V be the Volume of one sphere and V' be the Volume of second sphere.
⇒[tex]V = \frac{4}{3} \pi r^3[/tex] and [tex]V'= \frac{4}{3} \pi r'^3[/tex]
then;
[tex]\frac{V}{V'} =\frac{\frac{4}{3} \pi r^3}{\frac{4}{3} \pi r'^3} = \frac{r^3}{r'^3}[/tex]
⇒[tex]\frac{V}{V'} = \frac{(2r')^3}{r'^3}= \frac{8r'^3}{r'^3} = \frac{8}{1}[/tex]
V : V' = 8: 1
