Question

A bucket of height 8 cm and made up of copper sheet is in the form of frustum of a right circular cone
with radii of its lower and upper ends as 3 cm and 9 cm respectively. Calculate :
i) the height of right circular cone.
ii) the volume of water which can be filled in the bucket.
iii) the area of copper sheet required to make the bucket.
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Answer 1

Answer:

i) The height of the cone of which the bucket is a part of is 12 cm

ii) the volume of water which can be filled in the bucket is 312π cm³

iii) the area of metal sheet required to make the bucket is 129π cm²

Step-by-step explanation:

we have been given

h = 8 cm

r₁ = 9 cm

r₂ = 3 cm

Then slant height

L =

= √(8² + 6²)

= 10 cm

i) let h₁ be the height of the cone of which the bucket is a part of, so,

h₁ = hr₁/(r₁-r₂)

= 8 x 9/6

= 12 cm

ii) volume of the water which can be filled in the bucket

=

= 8π( 81 + 9 + 27)/3

= 8 x π x 117/3

= 312π cm³

iii) area of the metal sheet required to make the bucket = surface area

= πL(r₁ + r₂) + πr₂²

=π x 10 x 12 + 9π

= 129π cm²

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Step-by-step explanation: