Question

$\large\mathbf{HEY\: QUESTION❤}$

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, then find the radius and slant height of the heap?


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Answer 1

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Answer 2

✯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, then find the radius and slant height of the heap?

✯Solution✯

• According to question, Sand in cylindrical bucket is emptied to make a conical heap.
• So, Volume of cylindrical bucket =Volume of conical heap

✮Volume of cylindrical bucket✮

• Radius (r) = 18cm
• Height (h) = 32cm
• Volume (v) = πr²h
• Volume (v) = ²²⁄₇ × 18 × 18 × 32

✮Volume of conical heap✮

• Height (h) = 24cm
• Radius (r) = r cm
• Slant height (l) = l cm
• Volume (v) =⅓πr²h
• Volume (v) = ⅓πr²24
• Volume (v) = 8πr²

✶Volume of cylindrical bucket = Volume of conical heap✶

• π × 18 × 18 × 32 = 8πr²
• π × 18 × 18 × 32 ÷ 8π = r²
• r² = π × 18 × 18 × 32 ÷ 8π
• r² = 18 × 18 × 4
• r² = 1296
• r = √1296
• r = 36cm

          ✵Radius = 36cm

          ✵Slant height (l) = ?

• l² = h² + r²        (Pythagoras Theorem)
• l² = 24² + 36²
• l² = 576 + 1296
• l² = 1872
• l = √1872
• l = √12 × 12 × 13
• l = √12² × 13
• l = √12² × √13
• l = 12√13cm

          ✵Slant height = 12√13cm