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A cylindrical bucket of diameter 28 cm and height 12 cm is full of water. The water is emptied into a rectangular tub of length 66 cm and breadth 28 cm. Find the height to which water rises in the tub.  
Asked by Topperlearning User | 13 Oct, 2017, 01:56: PM
answered-by-expert Expert Answer

Given: Diameter of cylindrical vessel = 28 cm ⇒ radius of cylindrical vessel (R) = 14 cm

Height of cylindrical vessel (H) = 12 cm

Let V denote the volume of the cylindrical vessel.

                        

begin mathsize 12px style straight V space equals space πR squared straight H straight V space equals space 22 over 7 cross times 14 cross times 14 cross times 12 straight V space equals space 7392 space cm cubed end style

Length of the rectangular tub (l) = 66 cm

Breadth of the rectangular tub (b) = 28 cm

Let h be the height to which the water rises and V1 denote the volume of the rectangular tub.

                        

begin mathsize 12px style straight V subscript 1 space equals space lbh straight V subscript 1 space equals space 66 cross times 28 cross times straight h straight V subscript 1 space equals space 1848 straight h space cm cubed end style

Now, volume of water in the rectangular tub is equal to the volume of water in the cylindrical tub. Therefore,

begin mathsize 12px style straight V subscript 1 space equals space straight V 1848 straight h space equals space 7392 straight h space equals space 4 space cm end style

Answered by | 13 Oct, 2017, 03:56: PM

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