he radii of a frustum of a cone are 5 cm and 9 cm and height is 6 cm, then the volume is ..... cm³.select a proper option (a), (b), (c) or (d) from given options so that the statement becomes correct.
(a) 320????
(b) 151????
(c) 302????
(d) 98????
Answers
Answered by
9
Let R and r be the radii of the top and the base of the bucket respectively , and let h be the height.
Then, R = 9 cm , r = 5 cm and h = 6 cm.
Volume of the frustum of the cone = 1/3πh [ R² + r² + Rr ) cm³.
=> ( 1/3 × 22/7 × 6 ) × [ (9)² + (5)² + 9×5 ]
=> [ ( 22 × 2/7 ) × ( 81 + 25 + 45 ) ] cm³.
=> [ ( 44/7 ) × ( 151 ) ] cm³.
=> ( 44/7 × 151 ) cm³.
=> 474.57 cm³.
Then, R = 9 cm , r = 5 cm and h = 6 cm.
Volume of the frustum of the cone = 1/3πh [ R² + r² + Rr ) cm³.
=> ( 1/3 × 22/7 × 6 ) × [ (9)² + (5)² + 9×5 ]
=> [ ( 22 × 2/7 ) × ( 81 + 25 + 45 ) ] cm³.
=> [ ( 44/7 ) × ( 151 ) ] cm³.
=> ( 44/7 × 151 ) cm³.
=> 474.57 cm³.
Answered by
1
Option ( c ) is correct.
Explanation :
Dimensions of the frustrum :
r = 5 cm , R = 9 cm ,
Height ( h ) = 6 cm
Volume ( V ) = (πh/3 )[R²+Rr+r²]
=> V = π×6/3 )[9²+9×5+5²]
=> V = π× ( 2 × 151 )
=> V = 302π cm³
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