Question

39. The rain water collected on the roof of a building of
dimensions 22 mx 20 m, is drained into a cylindrical
vessel having base diameter 2 m and height 3-5 m. If
the vessel is full up of the brim. Find the height of
rain water on the roof.​

Answer 1

Hope this helps u......hmmmm

Answer 2

$\bold{\Huge{\underline{\boxed{\rm{\red{ANSWER\::}}}}}}$

$\bold{\Large{\underline{\sf{\green{Given\::}}}}}$

The rain water collected on the roof of a building of  dimensions 22mx20m, is drained into a cylindrical  vessel having base diameter 2m and height 3.5m. If  the vessel is full up of the brim.

$\bold{\Large{\underline{\sf{\pink{To\:find\::}}}}}$

The height of rain water on the roof.

$\bold{\Large{\underline{\sf{\purple{Explanation\::}}}}}$

$\bold{We\:have}\begin{cases}\sf{Length\:of\:roof=22m}\\ \sf{Breadth\:of\:roof=20m}\\ \sf{Cylindrical\:base\:diameter=2m}\\ \sf{Height\:of \:cylindrical\:vessel=3.5m}\end{cases}$

Formula used here;

• Volume of cylinder= πr²h   [cubic units]

• Volume of cuboid= Length×Breadth×Height   [cubic units]

→ Diameter of base,D= 2m

→ Radius of base,[r]= $\bold{\cancel{\frac{2}{2} }}$

→ Radius of base,[r]= 1m

Let the height of the roof be H m

If the vessel is full,then we can say that;

Volume of roof = volume of cylindrical vessel

→ L × B × H = πr²h

→ 22m × 20m × H = $\bold{\frac{22}{7} *(1m)^{2} *3.5m}$

→ 440 × H = $\bold{\frac{22}{\cancel{7}} *(1m)^{2} *\cancel{3.5m}}$

→ 440m² × H = 22× 1m² × 0.5m

→ 440m² × H = 11m³

→ H = $\bold{\cancel{\frac{11m^{3} }{440m^{2} }} }$

→ H = 0.025m

If convert into cm then;

⇒ $\boxed{1m\:=100cm}$

⇒ H = (0.025 × 100)cm

⇒ H = 2.5cm

Thus,

$\bold{\Large{\boxed{\sf{The\:height\:of\:rain\:water\:on\:the\:roof\:is\:2.5cm}}}}}$