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------------------------------------------------ Two heaps of rice are of similar shape and contain 250 kg and 128 kg of rice respectively. The height of the smaller heap is 56 cm. Find the height of the bigger heap.

Answer :

The relationship gives a height of approximately 70 cm for the bigger heap.

Since the heaps are similar in shape, their volumes are proportional to the cubes of their corresponding dimensions.

First, let's denote the height of the bigger heap as H. Given that the volumes are proportional to the weights of the rice heaps:

  • Volume of smaller heap: V1 = 128 kg
  • Volume of bigger heap: V2 = 250 kg
  • Height of smaller heap: h1 = 56 cm
  • Height of bigger heap: h2 = H

The ratio of the volumes (weights) of two similar objects is equal to the cube of the ratio of their corresponding heights (since V ∝ h³):

(H / 56)³ = 250 / 128

  • Simplify and solve for H:

First, find the volume ratio:
(H / 56)³ = (250 / 128)
(H / 56)³ = 1.953125

  • Take the cube root of both sides:
    H / 56 = ³√1.953125
    Calculate the cube root:
    H / 56 ≈ 1.25
    Finally, solve for H:
    H ≈ 1.25 × 56
  • ≈ 70 cm

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