an open metal bucket is in shape of a frustum mounted on a cylindrical base made of same metallic sheet the dia of two circular ends of bucket are 45 and 25 cm the total height of bucket is 40 cm and base of cylinder is 6cm find area of metallic sheet
Answers
Area of metallic sheet used = CSA of Frustum + CSA of Cylinder + CSA of Base
CSA of Frustum -
Diameter of the bigger circular end = 45 cm
Radius = 45/2 = 22.5 cm
Diameter of the smaller circular end = 25 cm
Radius = 25/2 = 12.5 cm
Height of the frustum = Total height of the bucket - Height of the circular base
⇒ 40 - 6 = 34 cm
Slant Height = l √h² + (r1² - r2²)²
⇒ √34² + (22.5 - 12.5)²
⇒ √1156 + (10)²
⇒ √1156 + 100
⇒ √1256
⇒ Slant Height = 35.44 cm
CSA of Frustum = π(r1 + r2)l
⇒ 22/7*(22.5 + 12.5)*35.44
⇒ 22/7*35*35.44
= 3898.4 cm²
Area of Circular Base -
Base is a circular part with radius 25/2 = 12.5 cm
Area of circular base = πr²
⇒ 22/7*12.5*12.5
491.07 cm²
CSA of Cylinder = 2πrh
⇒ 2*22/7*12.5*6
⇒ 471.428
Area of metallic sheet used = 3898.4 cm² + 491.07 cm² + 471.428
= 4860.898 cm²
Answer.
Area of metallic sheet used = curved surface area of Frustum + curved surface area of Cylinder + area of circular Base.
Diameter of the bigger circular end = 45 cm
Radius, r1 = 452= 22.5 cm
Diameter of the smaller circular end = 25 cm
Radius, r2 = 252=12.5 cm
Height of the frustum, h = Total height of the bucket (H) - Height of the circular base (h1)
= 40 - 6 = 34 cm
Slant Height of frustum (l) =h2+(r1−r2)2−−−−−−−−−−−−√
⇒l=342+(22.5−12.5)2−−−−−−−−−−−−−−−−√
⇒l=1156+(10)2−−−−−−−−−−√
⇒l=1156+100−−−−−−−−−√
⇒l=1256−−−−√
⇒ Slant Height, l = 35.44 cm
Curved surface area of Frustum = π(r1+r2)l
= 227×(22.5+12.5)×35.44
⇒227×35×35.44
= 3898.4 cm2
Area of Circular Base with radius 252=12.5 is given by,
Area of circular base = πr
=227×12.5×12.5
= 491.07 cm²
Curved surface area of Cylinder = 2πr2h1
= 2×227×12.5×6
= 471.428 cm²
Area of metallic sheet used = 3898.4 cm² + 491.07 cm² + 471.428 cm²
= 4860.898 cm²
Volume of water in bucket = Volume of Frustum
= 13πh(r21+r22+r1r2)
= 13×227×34(22.52+12.52+22.5×12.5) = 33615.48 cm³
Now, 1 litre = 1000 cm
Thus, Volume of water in bucket in litres = 33.62 litres