Q54 of 56 Page 13

The dimensions of a solid iron cuboid are 4.4 m 2.6 m 1.0 m. It is melted and recast into a hollow cylindrical pipe of 30 cm inner radius and thickness 5 cm. Find the length of the pipe.(CBSE 2017)

For Cuboid,


Length, l = 4.4 m


Breadth, b = 2.6 m


Height, h = 1 m


As we know,


Volume of cuboid = lbh


Where l, b and h are length, breadth and height of cuboid respectively.


⇒ Volume of given cuboid, V = 4.4(2.6)(1) = 11.44 m3


For cylindrical pipe that is recast from hemisphere,


Inner radius, r = 30 cm = 0.3 m [As, 1 m = 100 cm]

Outer radius, R = 30cm + 5cm = 35cm = 0.35m

Let the length of pipe(or height) = h


We know that,


Volume of hollow cylinder = π(R2 - r2)h

Volume of hollow cylinder = π [(0.35)2 - (0.30)2] × h = π. 0.032h


As the volume remains same, when a body is reformed to another body


Volume of cuboid = Volume of pipe


⇒ 11.44 = 0.032πh


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The diameters of the lower and upper ends of a bucket in the form of a frustum of a cone are 10 cm and 30 cm respectively. If its height is 24 cm, find :

(i) The area of the metal sheet used to make the bucket.


(ii) Why should we avoid the bucket made by ordinary plastic? [Use π = 3.14](CBSE 2018)