Question

A cylindrical bucket with the diameter 56cm and 24cm height ,is full of water. If the water is poured into a 88cm long and 42cm wide rectangular tank,find the height of the water level in the tank.

Answer 1

Answer:

16cm

Step-by-step explanation:

Diameter of cylinder = 56 cm then radius is 28 cm

Height of cylinder = 24 cm

Length of rectangular tank is 88cm

breadth of rectangular tank is 42cm

As water from cylindrical tank is emptied into rectangular tank

• so volume of cylindrical tank = volume of rectangular tank

• volume of cylindrical tank = πr^2h

• volume of rectangular tank =l×b×h

• πr^2h = l×b×h

Volumn of cylinder  = volumn of rectangular tank

π * r² * h = l * b * h

22/7 * 28² * 24 = 88 * 42 * h

After solving

h = 15.98 = 16 cm ( approx )

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Answer 2

Answer:

$\sf{The \ height \ of \ the \ water \ level} \\ \sf{in \ the \ tank \ is \ 16 \ cm}$

Given:

$\sf{For \ cylindrical \ bucket,} \\ \\ \sf{Diameter=56 \ cm \ [\therefore{Radius (r)=28 \ cm}],} \\ \\ \sf{Height(h)=24 \ cm} \\ \\ \sf{For \ cuboidal \ tank,} \\ \\ \sf{Length(l)=88 \ cm,} \\ \\ \sf{Breadth(b)=42 \ cm}$

To find:

$\sf{The \ height(H) \ of \ the \ water \ level} \\ \sf{in \ the \ tank.}$

Solution:

$\sf{Since, \ water \ is \ poured \ from \ bucket} \\ \\ \sf{to \ tank. \ Therefore, \ the \ volume \ of \ water \ in \ the \ tank} \\ \\ \sf{will \ be \ same \ as \ volume \ of \ the \ bucket.} \\ \\ \boxed{\sf{Volume \ of \ cylinder=Volume \ of \ cuboid.}} \\ \\ \sf{\therefore{\pi\times \ r^{2}\times \ h=l\times \ b\times \ H}} \\ \\ \sf{\pi\times28^{2}\times24=88\times42\times \ H}} \\ \\ \sf{H=\dfrac{22\times28\times28\times24}{7\times88\times42}} \\ \\ \\ \sf{H=\dfrac{413952}{25872}} \\ \\ \\ \sf{\longmapsto{H=16 \ cm}} \\ \\ \purple{\tt{\therefore{The \ height \ of \ the \ water \ level \ in}}} \\ \sf\purple{\tt{the \ tank \ is \ 16 \ cm}}$