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A cylindrical bucket, 32 cm high and with radius of base 18 cm, is filled with sand. This bucket is emptied on the ground and a conical heap of sand is formed. If the height of the - Mathematics

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Question

A cylindrical bucket, 32 cm high and with radius of base 18 cm, is filled with sand. This bucket is emptied on the ground and a conical heap of sand is formed. If the height of the conical heap is 24 cm. Find the radius and slant height of the heap.

Solution

Height (h1) of cylindrical bucket = 32 cm

Radius (r1) of circular end of bucket = 18 cm

Height (h2) of conical heap = 24 cm

Let the radius of the circular end of conical heap be r2.

The volume of sand in the cylindrical bucket will be equal to the volume of sand in the conical heap.

Volume of sand in the cylindrical bucket = Volume of sand in conical heap

`pixxr_1^2xxh_1=1/3pixxr_2^2xxh_2`

`pixx18^2xx32=1/3pixxr_2^2xx24`

`pixx18^2xx32= 1.3pixxr_2^2xx24`

`r_2^2= (3xx18^2xx32)/24 = 18^2 xx 4`

r2 = 18 x 2 = 36 cm

Slant height = `sqrt(36^2+24^2) = sqrt(12^2xx(3^2+2^2)) = 12sqrt13`

Therefore, the radius and slant height of the conical heap are 36 cm and

`12sqrt13` respectively

  Is there an error in this question or solution?

APPEARS IN

 NCERT Solution for Mathematics Textbook for Class 10 (2019 (Latest))
Chapter 13: Surface Areas and Volumes
Ex. 13.3 | Q: 7 | Page no. 252
 RD Sharma Solution for Class 10 Maths (2018 (Latest))
Chapter 14: Surface Areas and Volumes
Ex. 14.1 | Q: 69 | Page no. 32

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Solution A cylindrical bucket, 32 cm high and with radius of base 18 cm, is filled with sand. This bucket is emptied on the ground and a conical heap of sand is formed. If the height of the Concept: Conversion of Solid from One Shape to Another.
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