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CBSE Class 9 Answered

A solid rectangular block of iron of dimensions 7 cm x 4 cm x 2.75 cm is recast into a cylinder of radius 7 cm. Find the height of the recast cylinder.

Asked by Topperlearning User | 26 Oct, 2017, 11:52: AM
Expert Answer

Dimensions of the rectangular block are

Length (l) = 7 cm, breadth (b) = 4 cm and height (h) = 2.75 cm

Volume of the rectangular block (V) = lbh = 77 cm3

Radius of recast cylinder (R) = 7 cm

Let H be the height of the recast cylinder and V1 denotes its volume.

begin mathsize 12px style straight V space equals space πR squared straight H
straight V subscript 1 space equals space 22 over 7 cross times 7 cross times 7 cross times straight H
straight V subscript 1 space equals space 154 straight H space cm cubed end style

Rectangular block is recasted into a cylinder. Therefore volume of the cylinder is equal to the volume of the rectangular block.

begin mathsize 12px style straight V subscript 1 space equals space straight V
154 straight H space cm cubed space equals space 77 space cm cubed
straight H space equals space 77 over 154 space cm space equals space 1 half space cm space equals space 0.5 space cm end style

Thus, the height of the recast cylinder is 0.5 cm.

Answered by | 26 Oct, 2017, 01:52: PM
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