Question

A cuboid of dimensions 14cm*8 cm*7cm is completely immersed in a cubical trough of side 28cm, containing water to a height 20cm. What will be the height of water after the immersion? ​

Answer 1

Answer:

Height of the water will be 21 cm after the cuboid is immersed in the trough.

Step-by-step explanation:

Let the height of the water in the cubical trough is h cm after the immersion of the cuboid.

Volume of cuboid with dimensions 14cm×8cm×7cm will be

V = 14 × 8 × 7

V = 784 cm³

When this cuboid immersed in the water volume of water displaced = volume of the cuboid.

Initial height of the water in the trough = 20 cm

Increase in the height of the water = (h - 20) cm

Volume of the water displaced = 28×28×(h - 20)

And (28)²(h - 20) = 784

784(h -20) = 784

h - 20 = $\frac{784}{784}$

h - 20 = 1

h = 20 + 1

h = 21 cm

Therefore, height of the water after the immersion of cuboid will be 21 cm.

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Answer 2

Let the height of the water in the cubical trough is h cm after the immersion of the cuboid.

Volume of cuboid with dimensions 14cm×8cm×7cm will be

V = 14 × 8 × 7

V = 784 cm³

When this cuboid immersed in the water volume of water displaced = volume of the cuboid.

Initial height of the water in the trough = 20 cm

Increase in the height of the water = (h - 20) cm

Volume of the water displaced = 28×28×(h - 20)

And (28)²(h - 20) = 784

784(h -20) = 784

h - 20 = \frac{784}{784}

784

784

h - 20 = 1

h = 20 + 1

h = 21 cm