Question

A rectangular vessel of dimensions 30 cm x 22 cm x 10 cm is completly filled with water. This
water is poured completely into a conical vessel of base diameter 30 cm Find the height of
the water in the conical vessel.​

Answer 1

AnswEr :

Height = 28 cm.

$\bf{\Large{\underline{\sf{Given\::}}}}$

A rectangular vessel of dimensions 30 cm × 22 cm × 10 cm is completely filled with water. This water is poured completely into a conical vessel of base diameter 30 cm.

$\bf{\Large{\underline{\sf{To\:find\::}}}}$

The height of the water in the conical vessel.

$\bf{\Large{\underline{\rm{\red{Explanation\::}}}}}$

We have;

$\bf{Rectangular\:vessel\:of\:dimensions}\begin{cases}\sf{Length\:(l)=30cm}\\ \sf{Breadth\:(b)=22cm}\\ \sf{Height\:(h)=10cm}\end{cases}}$

$\bigstar$ Formula use :

$\bf{\large{\boxed{\sf{Volume\:of\:Cuboid\:=\:L*B*H}}}}}}$

$\implies\sf{Volume\:=\:(30*22*10)cm^{3} }\\\\\\\implies\sf{\orange{Volume\:=\:6600cm^{3} }}$

Now,

We have conical vessel diameter is 30 cm

$\leadsto\sf{Radius\:(r)=\:\dfrac{Diameter}{2} }\\\\\\\leadsto\sf{Radius\:(r)\:=\:\cancel{\dfrac{30}{2}cm }}\\\\\\\leadsto\sf{\orange{Radius\:(r)\:=\:15cm}}$

$\bigstar$ Formula use :

$\bf{\large{\boxed{\sf{Volume\:of\:Cone\:=\:\frac{1}{3} \pi r^{2} h}}}}}}$

A/q

$\implies\sf{\dfrac{1}{\cancel{3}} *\dfrac{22}{7} *\cancel{15}*15*h=6600}\\\\\\\\\implies\sf{\dfrac{22}{7} *5*15*h=6600}\\\\\\\\\implies\sf{22*75*h=6600*7}\\\\\\\\\implies\sf{h\:=\:\dfrac{\cancel{6600}*7}{\cancel{22}*75} }\\\\\\\\\implies\sf{h\:=\:\dfrac{\cancel{300}*7}{\cancel{75}} }\\\\\\\\\implies\sf{h\:=\:(4*7)cm}\\\\\\\\\implies\sf{\orange{h\:=\:28\:cm}}$

Thus,

$\bigstar$The height of the water in the conical vessel is 28 cm.

Answer 2

QUESTION:-

A rectangular vessel of dimensions 30 cm x 22 cm x 10 cm is completly filled with water. This

water is poured completely into a conical vessel of base diameter 30 cm Find the height of

the water in the conical vessel.

SOLUTION:-

we know that,

➠ Volume of cuboid = L ×B ×H

➠ volume of cuboid = 30cm ×22cm ×10cm

➠ volume of cuboid = 6600cm³

➠ .°. volume = 6600cm³.

NOW,

Given, the conical vessel diameter is 30cm.

➠ r = d/2

➠r = 30/2

➠ r = 15cm.

here,

➠ Volume of cone = ⅓πr²h

➠ 6600 = ⅓ ×22/7 ×(15)²×h

➠ h = 6600 ×7 / 22×75

➠ h = 88 ×7 /22

➠ h = 4 ×7

➠ h = 28cm

.°. the height of the water in the conical vessel is 28cm.