A metallic cylinder has radius 3 cm and height 5 cm.

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asked Mar 27 in Class X Maths by muskan15 (-2,337 points)

A metallic cylinder has radius 3 cm and height 5 cm. It is made of metal A. To reduce its weight, a conical hole is drilled in the cylinder, as shown and it is completely filled with a lighter metal B. The conical hole has a radius of 3/2 cm and its depth is 8/9 cm. Calculate the ratio of the volume of the metal A to the volume of the metal B in the solid .

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answered Mar 27 by navnit40 (-2,975 points)

Volume of metal A = Volume of the cylinder – volume of the cone

= π(3)2 × 5 – 1/3π × (3/2)2 × 8/9

= π(45 – 2/3)

= 133/3π cm3

Volume of metal B = Volume of the conical cavity

1/3 × (3/2)2  × 8/9 = 2/3π

Hence, ratio of the volume of the metal A to the volume of the metal B = (133π/3)/(2π/3) = 133/2

= 66.5 : 1

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