Question

A conical tent has the area of its base 154sq m. And its csa as 550sq.m.find volume of a tent

Answer 1

Base area = 154 m² and curve surface area = 550 m²

area of curve surface = 550 m²
area of curve surface of cone = πrl
here, r is the radius of cone and l is the lateral length of cone.
 550 = 22/7rl
 rl = 550 × 7/22 = 25 × 7 ----------------------(1)
and cross section area of it = 550 m²
area of CSA = πr² = 154 m²
22/7r² = 154 m²
⇒ r² = 154 × 7/22 = 49
⇒ r = 7m, put it in equation (1) 
l = 25m 
 now, h =√{l² - r²} 
so, h = √{25² - 7²} = 24m

hence, volume of conical  tent = πr²h/3 
  = 22/7 × 7² × 24/3 m³
  = 22 × 7 × 8 m³
  = 22 × 56 m³
  = 1232 m³

Answer 2

hiii!!!

here's ur answer...

area of the base of the conical tent = 154m²

we know that the base of a cone is circle.

therefore πr² = 154m²

==> 22/7 × r² = 154m²

==> r² = 154/1 × 7/22

==> r² = 7 × 7

==> r² = 49

==> r = √49

==> r = 7m

radius of the base of the conical tent is 7m.

now,

CSA of the cone is given = 550m²

therefore πrl = 550m²

==> 22/7 × 7 × l = 550m²

==> 22 × l = 550m²

==> l = 550/22

==> l = 25m

length of the conical tent is 25m.

height of the cone :-

by Pythagoras thereom...

a² + b² = c² ( a = r , b = h , c = l )

==> 7² + b² = 25²

==> 49 + b² = 625

==> b² = 625 - 49

==> b² = 576

==> b = √576

==> b = 24

hence, the height of the conical tent is 24m

volume of the conical tent = 1/3πr²h

= 1/3 × 22/7 × 7 × 7 × 24

= 22 × 7 × 8

= 1232m³

hope this helps..!!