A rectangular vessel of dimensions 20 cm × 16 cm × 11 cm is full of water. This water is poured into a conical vessel. The top of the conical vessel has its radius 10 cm. If the conical vessel is filled completely, determine its height.
Answers
Answer:
The height of the conical vessel is 33.6 cm.
Step-by-step explanation:
SOLUTION :
Given :
Length of a rectangular vessel, l = 20 cm
Breadth of a rectangular vessel, b = 16 cm
Height of a rectangular vessel, h = 11 cm
Radius of a conical vessel, r = 10 cm
Here, water from rectangular vessel (cuboid) is poured into a conical vessel.
Let, the height of a conical vessel be H
Volume of cuboid = volume of conical vessel
l × b × h = ⅓ πr²H
20 × 16 × 11 = ⅓ × 22/7 × 10² × H
20 × 16 × 11 = ⅓ × 22/7 × 100 × H
H = (20 × 16 × 11 × 3 × 7) / (100 × 22)
H = (16 × 11 × 3 × 7) / (5 × 22)
H = 3696/110 = 33.6 cm
Hence , the height of the conical vessel is 33.6 cm.
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Answer:
Step-by-step explanation:
Volume filled by water in rectangular vessel is
20*16*11=3520
Volume occupied by water in conical vessel is
1/3πr²h
=1/3*22/7*10*10*h
Equating volumes in rectangular and conical vessel,
We get
h=33.6cm