Answer:
Let S
1
be the original surface area of the sphere and S
2
be the surface area with double the diameter.
Doubling the diameter means doubling the radius. Let r
and r
corresponding radii.
We know that S=4πr
=2r
....Given
Hence,
S
=
4πr
⇒
(2r
)
r
⇒S
=4S
So, doubling radius will increase S by a factor of 4.
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Answers & Comments
Answer:
Let S
1
be the original surface area of the sphere and S
2
be the surface area with double the diameter.
Doubling the diameter means doubling the radius. Let r
1
and r
2
corresponding radii.
We know that S=4πr
2
and r
2
=2r
1
....Given
Hence,
S
2
S
1
=
4πr
2
2
4πr
1
2
⇒
S
2
S
1
=
(2r
1
)
2
r
1
2
⇒S
2
=4S
1
So, doubling radius will increase S by a factor of 4.