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Standard IX
Mathematics
Curved surface area of a Right Circular cone
Question
Find the slant height and vertical height of a cone with radius
5.6
cm
and curved surface area
158.4
cm
2
9
cm
and
8.07
cm
9
cm
and
7.05
cm
8
cm
and
8.07
cm
None of the above
A
8
cm
and
8.07
cm
B
None of the above
C
9
cm
and
8.07
cm
D
9
cm
and
7.05
cm
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Solution
Verified by Toppr
Given, Radius
=
5.6
cm
and curved surface area
=
158.4
cm
2
Let vertical height
=
h
, slant height
=
l
Then,
Curved surface area of cone
=
π
r
l
⇒
22
7
×
5.6
×
l
=
158.4
⇒
l
=
158.4
×
7
22
×
5.6
=
18
2
=
9
cm
We know,
l
2
=
r
2
+
h
2
.
Thus
h
2
=
l
2
−
r
2
=
9
2
−
(
5.6
)
2
=
81
−
31.36
=
49.64
.
Therefore,
h
=
√
49.64
⟹
h
=
7.05
cm
(approx.)
Hence, option
B
is correct.
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Similar Questions
Q1
Find the slant height and vertical height of a cone with radius
5.6
cm
and curved surface area
158.4
cm
2
View Solution
Q2
Find the curved surface area of a cone whose base radius is
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and slant height is
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Q3
A cone has a slant height of 9 cm and a base of radius of 7 cm. Find (i) its curved surface area (ii) total surface area.
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Q4
Find the curved surface area of a cone with a radius of
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and a slant height of
14
c
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.
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Q5
The diameter of a cone is
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and its slant height is
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. Find the area of its curved surface.
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