A bucket of height 20cm and made up of a metal sheet is in the form of frustum of a right circular cone with radii of its lower and upper ends as 3 cm and 15cm respectively. calculate the height of con of which the bucket is a part
Answers
The height of cone of which the bucket is a part is 25 cm.
Step-by-step explanation:
Let’s make assumptions from the attached figure below,
“h” = AO = height of the large cone
“x” = AD = height of the smaller cone
“y” = DO = height of the bucket = 20 cm (given)
“R” = OC = radius of the base of the large cone or the bucket = 15 cm (given)
“r” = DF = radius of the base of the smaller cone = 3 cm (given)
Now, let’s consider ∆ ADF and ∆ AOC, we have
∠A = ∠A …… [common angle]
∠ADF = ∠AOC ……. [corresponding angles, since EF//BC]
∴ By AA similarity, ∆ ADF ~ ∆ AOC
Since the corresponding sides of two similar triangles are proportional to each other.
∴ AD/AO = DF/OC
Substituting the given and assumed values from above
⇒ x/h = r/R = 3/15
⇒ x/(x+y) = 1/5
⇒ x/(x+20) = 1/5 ….. [since y = 20 cm]
⇒ 5x = x + 20
⇒ 5x – x = 20
⇒ 4x = 20
⇒ x =20/4
⇒ x = 5 cm ← height of the smaller cone
Thus,
The height of the larger cone “h” of which the bucket is a part is given by,
= x + y
Substituting x = 5 and y = 20
= 5 + 20
= 25 cm
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