A metallic bucket opens at the top with height 24cm in the form of a frustum of a cone and the radii of whose lower and upper circles ends are 7cm and 14cm respectively find the volume of the water wch can completely fill the bucket and the area of the metal sheet used to make the bucket
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Volume of Frustum(Bucket) = 1/3 πh(R²+r²+Rr)
= 1/3 × 22/7 × 24 ×(14²+7²+14(7))
= 22/7 × 8 × (196+49+98)
= 22/7 × 8 × 343
= 22 × 8 × 49
= 8624 cm³.
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Area of metal sheet required = CSA of Hemisphere + Area of Base
= πl(R+r) + πr²
l =√h²+(R-r)²
l = √24²+(14-7)²
l = √576+49
l = √625 ⇒ l = 25 cm
= 22/7 × 25 × (14+7) + (22/7 × 7 × 7)
= 22/7((25 × 21) + (7 × 7)
= 22/7(525+49)
= 22/7 × 574
= 22 × 82
= 1804 cm²
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= 1/3 × 22/7 × 24 ×(14²+7²+14(7))
= 22/7 × 8 × (196+49+98)
= 22/7 × 8 × 343
= 22 × 8 × 49
= 8624 cm³.
___________________________________________________________
Area of metal sheet required = CSA of Hemisphere + Area of Base
= πl(R+r) + πr²
l =√h²+(R-r)²
l = √24²+(14-7)²
l = √576+49
l = √625 ⇒ l = 25 cm
= 22/7 × 25 × (14+7) + (22/7 × 7 × 7)
= 22/7((25 × 21) + (7 × 7)
= 22/7(525+49)
= 22/7 × 574
= 22 × 82
= 1804 cm²
__________________________________________________________
☺ ☺ ☺ Hope this Helps ☺ ☺ ☺
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