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Maths-

General

Easy

Question

The diameter of the ends of a bucket of height 24 cm are 42 cm and 14 cm
respectively .Find the capacity of the bucket

16016 cm³
1616 cm³
6016 cm³
61160 cm³

hint Hint:

Volume of frustum of cone = $fraction numerator pi h over denominator 3 end fraction open square brackets fraction numerator open parentheses R cubed minus r cubed close parentheses over denominator R minus r end fraction close square brackets$

The correct answer is: 16016 cm³

We have given the dimensions of a bucket which is of frustrum shape
Top diameter = 42 cm
Top radius, R = 21 cm
Bottom diameter = 14
Bottom radius, r = 7 cm
Height of frustrum , h = 24 cm
Therefore capacity of bucket = volume of bucket
$equals fraction numerator pi h over denominator 3 end fraction open square brackets fraction numerator open parentheses R cubed minus r cubed close parentheses over denominator R minus r end fraction close square brackets$
$equals fraction numerator left parenthesis 22 divided by 7 right parenthesis left parenthesis 24 right parenthesis over denominator 3 end fraction open square brackets fraction numerator open parentheses 21 cubed minus 7 cubed close parentheses over denominator 21 minus 7 end fraction close square brackets$
= $left parenthesis 22 right parenthesis left parenthesis 8 right parenthesis open square brackets fraction numerator open parentheses 21 cubed minus 7 cubed close parentheses over denominator 7 cross times 14 end fraction close square brackets$
= $left parenthesis 176 right parenthesis open square brackets fraction numerator left parenthesis 9261 minus 343 right parenthesis over denominator 98 end fraction close square brackets$
= $left parenthesis 176 right parenthesis open square brackets fraction numerator left parenthesis 8918 right parenthesis over denominator 98 end fraction close square brackets$
= 176 × 91

$equals 16016 cm cubed$
Therefore, the correct option is a)16016 cm³

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