Question

A cone of height 8 mhas a curved surface area of 188.4 square meters.find its volume.

Answer 1

CSA = 118.4 sq.m
CSA = π r L

L = $\sqrt{ r^{2}+ h^{2} }$

CSA = π r ($\sqrt{ r^{2}+ h^{2} }$)

118.4 =3.14* r ($8^{2} + r^{2}$)

$\frac{118.4}{3.14}$=r* ($8^{2} + r^{2}$)

60 = r * (64 + $r^{2}$)

Squaring both the sides,

3600 = $r^{2}(64+ r^{2})$

3600 = 64$r^{2}+ r^{4}$

$r^{4}+64 r^{2}-3600=0$

Now lets take $r^{2} = x [tex] x^{2} + 64 x - 3600$ = 0

[tex] x^{2} +100x-36x-3600=0

x(x+100)-36(x+100) = 0[/tex]

(x+100)(x-36) = 0

x = -100,36

$^{2}$ = 36 (only positive value)

Volume = 1/3 π $r^{2}$h

=1/3 * 3.14 * 6 * 6 * 8

=301.44 $m^{3}$

Answer 2

Answer:

Step-by-step explanation:

Ace

CSA = 118.4 sq.m

CSA = π r L

L = 

CSA = π r ()

118.4 =3.14* r ()

=r* ()

60 = r * (64 + )

Squaring both the sides,

3600 = 

3600 = 64

Now lets take  = 0

(x+100)(x-36) = 0

x = -100,36

= 36 (only positive value)

Volume = 1/3 π h

=1/3 * 3.14 * 6 * 6 * 8

=301.44 

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