Question
Asked Sep 5, 2019
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A rectangular solid measures 1.0 m by 5.6 cm by 2.1 dm. Express its volume in cubic meters, liters, cubic inches, and cubic feet

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Expert Answer

Step 1

The volume of the rectangle can be calculated by the formula,

Volume (V) = length (l) × width (b) × height (h)  ………(1)

Given that,

Length of the rectangular solid is 1.0 m

Width of the rectangular solid is 5.6 cm

Height of the rectangular solid is 2.1 dm

First, convert all the sides in the unit of meter by using the following conversion data as follows:

1 cm = 10-2 m

Therefore, 5.6 cm is equal to 5.6×10-2 m

1 dm = 10-1 m

Therefore, 2.1 dm is equal to 2.1×10-1 m

Now calculate the volume of the rectangular solid by using the equation (1) as follows:

Thus the volume of the rectangular solid is 1.18 ×10-2 cubic meters.

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volume (V) 1.0m x 5.6x102m x 2.1 x 101m 11.76 x 10-3m3 1.18 x 102cubic meters

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Step 2

Now the volume is to be calculated in liters.

As it is known as,

1 liter is equal to 1 dm3

Convert all the units in dm3 as follows:

Since 1 m is equal to 10 dm

1 cm is equal to 10-1 dm

Therefore, 5.6 cm is equal to 5.6×10-1 dm

Now calculate the volume of the rectangular solid by substituting these values in equation (1) as follows:

Therefore, the volume of the rectangular solid in liter is 11.76 liter

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Volume (V 10 dm x 5.6 x 10" dm x 2.1 dm =11.76 dm3 since 1dm3 1 liter =11.76 liter

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Step 3

Now volume is to be calculated in cubic inches.

Convert all the given lengths in inches.

1 m is equal to 39.37 inches

 Since 5.6 cm is equal to 5.6 × 10-2 m

Therefore 5.6 cm in inches is,

(5.6 × 10-2 × 39.37) inches

=220.47 × 10-2 inches

Now convert 2.1 dm in inches as follows:

2.1 dm is equal to 2.1 × 10-1 m.

Or 2.1 dm is ...

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Volume V39.37 inches x 220.47 x 102 inches x 82.68 x 10-1 inches =7.18x102 cubic inches

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