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Byju's Answer
Standard VII
Mathematics
Radii, Chord, Diameter and Circumference of the Circle
A circular me...
Question
A circular metal plate expends under heating so that its radius increases by k%. Find the approximate increase in the area of the plate, if the radius of the plate before heating is 10 cm.
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Solution
Let at any time, x be the radius and y be the area of the plate.
Then
,
y
=
x
2
Let
∆
x
be
the
change
in
the
radius
and
△
y
be
the
change
in
the
area
of
the
plate
.
We
have
∆
x
x
×
100
=
k
When
x
=
10
,
w
e
g
e
t
∆
x
=
10
k
100
=
k
10
Now
,
y
=
π
x
2
⇒
d
y
d
x
=
2
π
x
⇒
d
y
d
x
x
=
10
cm
=
20
π
cm
2
/
cm
∴
∆
y
=
d
y
=
d
y
d
x
d
x
=
20
π
×
k
10
=
2
k
π
cm
2
Hence, the approximate change in the area of the plate is 2k
π
cm
2
.
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