4. The radius of a sphere is increased by p%. By what
per cent its surface area increases?
Answer:
Answers
Answered by
1
Step-by-step explanation:
ANSWER
The surface area of a sphere is 4πr
2
If radius increases by p%
The new radius will be r(1+
100
p
)
So, the new surface area will be r
2
(1+
100
p
)
2
∴% change in surface area
=
4πr
2
4πr
2
(1+
100
p
)
2
−4πr
2
×100
=[(1+
100
p
)
2
−1]×100
=(1+
100
2
p
2
+
100
2p
−1)×100
=(
100
2
p
2
+
100
2p
)×100
=
100
p
2
+2p
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