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A cone of height 24cm has a curved surface area 550 cm2. Find its volume.

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1232 cm3

1600 cm3

1334 cm3

1200 cm3

answer is A.

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Detailed Solution

Surface area of cone = 550 cm2
Height = 24 cm
Curved surface area (CSA) = πrl
Slant height, l = √r2+h2
:. CSA = π r (√ r2+h2)
550 = π r ( √r2+(24)2)
550 =

\frac{22}{7}

r (√ r2+576)
r(√r2+576) = 550

\times \frac{7}{22}

r(√r2+576) = 25

\times

7
on squaring both the sides
r2 ( r2 + 576) = 252

\times

72
r4 +576 r2 - (625

\times

49) = 0
r4 +625 r2 - 49 - (625

\times

49) = 0
(r2 +625) (r2 - 49) = 0
r2 + 625 =0
r2 = - 625 which is not possible
r2 = 49
r = 7
Thus, the radius of the cone = 7 cm
Volume; V =

\frac{1}{3}

π r2 h
V =

\frac{1}{3} \times \frac{22}{7} \times

\times

\times

24
V = 22

\times

\times

8
V = 1232 cm3

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