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Answer :
Final answer:
The length of a block of cobalt metal having a mass of 546.8 g, a height of 1.06 cm, and a width of 37.6 mm (or 3.76 cm) is 0.146 m.
Explanation:
To find the length of a block of cobalt metal, we can use the formula for density, which is mass divided by volume (Density = Mass/Volume). We know the mass of the cobalt block (546.8 g), the density of cobalt (8.86 g/cm³), the height (1.06 cm), and the width (37.6 mm or 3.76 cm) of the block.
Volume of the cobalt block can be calculated from its given mass and density using the formula Volume = Mass/Density. Thus, the volume of the cobalt block is 546.8 g / 8.86 g/cm³ = 61.69 cm³.
Now, the volume of a rectangular block is also given by the formula Volume = Length x Width x Height. Using this formula and substituting the given and calculated values, we get 61.69 cm³ = Length x 3.76 cm x 1.06 cm.
By solving for Length, we get Length = 61.69 cm³ / (3.76 cm x 1.06 cm) = 14.6 cm. Since the question seeks the answer in meters, we convert 14.6 cm to meters by dividing by 100 (as there are 100 cm in a meter), resulting in a Length of 0.146 m.
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