an industrial metallic bucket is the shape of the frustum of a right circular whose top and bottom diameter are 10cm and 4m and whose height is 4m find tsa and csa of bucket
Answers
R=10cm,r=4cm,h=4cm
l= (R−r) 2+h2
= (10−4) 2+(4)2=
= (10)2+(4)2-2×10×4
=100+16-80= 116-80=36+16= √52
=7.2cm
CSA = π(R+r)l=π(10+4)×7.1=100.8πcm2
TSA = πl(R+r)+π(R2+r2)
=100.8π+π(10 2 +4 2)
= 100.8π+116π=216.8πcm2
Answer:
The total surface area of the bucket is approximately 109.76 square meters
The curved surface area is approximately 100.10 square meters.
Step-by-step explanation:
We can start by first finding the slant height of the frustum using the Pythagorean theorem:
s = √(r₁ - r₂)² + h²
where r₁ is the radius of the bottom base, r₂ is the radius of the top base, and h is the height of the frustum.
Given the dimensions of the bucket, we have:
r₁ = 2 m (since the bottom diameter is 4 m)
r₂ = 5 cm = 0.05 m (since the top diameter is 10 cm)
h = 4 m
Therefore, the slant height is:
s = √(2 - 0.05)² + 4² ≈ 4.002 m
Next, we can use the formulas for the total surface area (TSA) and curved surface area (CSA) of a frustum:
TSA = π(r₁ + r₂)s + πr₁² + πr₂²
CSA = π(r₁ + r₂)s
Substituting the values we have, we get:
TSA = π(2 + 0.05)(4.002) + π(2²) + π(0.05²) ≈ 109.76 m²
CSA = π(2 + 0.05)(4.002) ≈ 100.10 m²
Therefore, the total surface area of the bucket is approximately 109.76 square meters, and the curved surface area is approximately 100.10 square meters.
To know more about Pythagorean theorem refer :
https://brainly.in/question/54142264
https://brainly.in/question/54161317
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