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empt mins 10 days ago Bookwork code: Report issue with this quest volume of a sphere=(4)/(3)pi r^3 where I is the radius. Zinc has a density of 7.135g/cm^3 How many kilograms would a sphere of zinc with a radius of 8 cm weigh? Give your answer to 1 d.p

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empt
mins 10 days ago
Bookwork code:
Report issue with this quest
volume of a sphere=(4)/(3)pi r^3 where I is the radius.
Zinc has a density of 7.135g/cm^3
How many kilograms would a sphere of zinc with a radius of 8 cm weigh?
Give your answer to 1 d.p

empt mins 10 days ago Bookwork code: Report issue with this quest volume of a sphere=(4)/(3)pi r^3 where I is the radius. Zinc has a density of 7.135g/cm^3 How many kilograms would a sphere of zinc with a radius of 8 cm weigh? Give your answer to 1 d.p

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FelixElite · Tutor for 8 years

Answer

The weight of the sphere of zinc is approximately \(15.3 \, \text{kg}\).

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## Step 1:<br />The volume of a sphere can be calculated using the formula:<br />### **\(V = \frac{4}{3} \pi r^3\)**<br />where \(V\) is the volume, \(\pi\) is a constant (approximately 3.14159), and \(r\) is the radius of the sphere.<br /><br />## Step 2:<br />Substitute the given radius \(r = 8 \, \text{cm}\) into the formula to calculate the volume.<br />### **\(V = \frac{4}{3} \pi (8)^3\)**<br />### **\(V = \frac{4}{3} \pi (512)\)**<br />### **\(V = \frac{2048}{3} \pi\)**<br />### **\(V \approx 682.67 \pi\)**<br />### **\(V \approx 2144.66 \, \text{cm}^3\)**<br /><br />## Step 3:<br />Zinc has a density of \(7.135 \, \text{g/cm}^3\). The mass \(m\) of the sphere can be calculated using the formula:<br />### **\(m = \text{density} \times \text{volume}\)**<br />### **\(m = 7.135 \, \text{g/cm}^3 \times 2144.66 \, \text{cm}^3\)**<br />### **\(m \approx 15300.47 \, \text{g}\)**<br /><br />## Step 4:<br />Convert the mass from grams to kilograms by dividing by 1000.<br />### **\(m \approx 15300.47 \, \text{g} \div 1000\)**<br />### **\(m \approx 15.30 \, \text{kg}\)**<br /><br />## Step 5:<br />Round the result to 1 decimal place as required.<br />### **\(m \approx 15.3 \, \text{kg}\)**
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