Question

A conical tent has area of base as 154square m and it's curved surface area as 550 sq. m. Find the volume of tent

Answer 1

area of base = πr²
= 3.14 x r² = 154
r² = 154/3.14
r² = 49 m
and r = 7 m

Now we have radius of cone = 7m
csa of cone = πrl
3.14 x 7 x l = 550
l = 550/3.14 x 7

l = 21.98 m

, Now, volume of cone = πr²h/3

h² = l² - r²
h²= 21.98 ² - 7²
h² = 483 - 49
h²= 434
h = √434 = 20.83m

now, πr²h/3

3.14 x 7x7x 20.83 / 3
= 9536/3
= 3178 m³

Answer 2

given

area of base of  tent(conical) = 154m^2

curve surface area of tent = 550m^2

find = volume of tent

area of base of tent = πr^2

154 = 22/7*r^2

154*7/22=r^2

49 = r^2

r = √49

r = 7m

Also,

curved surface area of tent = πrl

550 = 22/7*7*l                        (7 is cut)

550/22 = l

l = 25m

but for volume we needed height

By pythagoras theorem

l^2 = h^2 + r^2

25^2 = h^2 + 7^2

625 = h^2 + 49

H^2  = 625 - 49

h^2 = 576

h = 24m

NOW,

volume of tent = 1/3*πr^2*h

= 1/3*22/7*7*7*24

=1/3*22*7*24

= 22*7*8

=1232m^3