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A sculptor needs to lift a piece of marble. It is a cuboid with dimensions 1 m by 0 .9 m by 0 .25 m. Marble has a density of 2.7g/cm^3 What is the mass of the marble in kg?Optional working

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A sculptor needs to lift a piece of marble. It is a cuboid with dimensions 1 m by 0 .9 m by 0 .25 m. Marble has a density of 2.7g/cm^3 What is the mass of the marble in kg?Optional working

A sculptor needs to lift a piece of marble. It is a cuboid with dimensions 1 m by 0 .9 m by 0 .25 m. Marble has a density of 2.7g/cm^3 What is the mass of the marble in kg?Optional working

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RussellElite · Tutor for 8 years

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### Step 1: <br />The volume of the marble is \( \text{Volume} = 1 \mathrm{~m} \times 0.9 \mathrm{~m} \times 0.25 \mathrm{~m} = 0.225 \mathrm{~m}^{3} \).<br /><br />### Step 2: <br />The dimensions of the marble in centimeters are \( 100 \mathrm{~cm} \), \( 90 \mathrm{~cm} \), and \( 25 \mathrm{~cm} \).<br /><br />### Step 3: <br />The volume of the marble in cubic centimeters is \( \text{Volume} = 100 \mathrm{~cm} \times 90 \mathrm{~cm} \times 25 \mathrm{~cm} = 225000 \mathrm{~cm}^{3} \).<br /><br />### Step 4: <br />The mass of the marble in grams is \( \text{Mass} = 2.7 \mathrm{~g/cm}^{3} \times 225000 \mathrm{~cm}^{3} = 607500 \mathrm{~g} \).<br /><br />### Step 5: <br />The mass of the marble in kilograms is \( \text{Mass} = 607500 \mathrm{~g} \div 1000 = 607.5 \mathrm{~kg} \).

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## Step 1: <br />First, we need to calculate the volume of the marble. Since the marble is in the shape of a cuboid, we can use the formula for the volume of a cuboid, which is \( \text{Volume} = \text{Length} \times \text{Width} \times \text{Height} \).<br /><br />## Step 2: <br />The dimensions of the marble are given in meters, but the density is given in grams per cubic centimeter. Therefore, we need to convert the dimensions from meters to centimeters. There are 100 centimeters in a meter, so we multiply each dimension by 100.<br /><br />## Step 3: <br />Now that we have the dimensions in the same units, we can calculate the volume of the marble in cubic centimeters.<br /><br />## Step 4: <br />Next, we calculate the mass of the marble. The mass of an object is obtained by multiplying its density by its volume. So, we multiply the volume of the marble by its density.<br /><br />## Step 5: <br />Finally, we need to convert the mass from grams to kilograms, since the question asks for the mass in kilograms. There are 1000 grams in a kilogram, so we divide the mass in grams by 1000 to get the mass in kilograms.
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