Question

A metal cuboid of dimension 22cm *15cm*7.5cm was melted and cast into a cylinder of heights and 14cm what is it's radius

Answer 1

$<b>Heya mate. (^_-). Solution below.$
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• Given length of the cuboid = 22 cm

• Given breadth of the cuboid = 15 cm

• Given height of the cuboid = 7.5 cm



• Then, volume of the cuboid

= length × breadth × height

= 22 × 15 × 7.5

= 2475 cm³



• Now, the cuboid is melted into a cylinder.

So, volume of cuboid will be equal to volume of cylinder


• Then, volume of cylinder = 2475 cm³




• But, volume of any cylinder = πr²h, where π = 22/7, r is radius of cylinder and h is height of cylinder.

=> 2475 = πr²h

=> 2475 = 22/7 × r² × h

• Given height of cylinder = 14 cm

=> 2475 = 22/7 × r² × 14

=> 2475 × 7/22 × 1/14 = r²

=> 2475 × 7/308 = r²

=> 17325/308 = r²

=> 56.25 = r²

=> √56.25 = r

=> √(7.5 × 7.5) = r

=> r = 7.5 cm

$<marquee>Hence, the radius of the cylinder is 7.5 cm.</marquee>$
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Thank you.. ;-)