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An open container made up of a metal sheet is in the form of a frustum of a cone of height 8 cm with radii of its lower and upper ends as 4 cm and 10 cm respectively. The cost of the oil at the rate of Rs. 50 per litre, which can completely fill the container, will be
- a)Rs. 45.60
- b)Rs. 76.50
- c)Rs.65.50
- d)Rs.70
Correct answer is option 'C'. Can you explain this answer?
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An open container made up of a metal sheet is in the form of a frustum...
Volume of the Frustum of a Cone
To find the cost of the oil needed to fill the frustum, we first need to calculate its volume. The formula for the volume of a frustum of a cone is:
Volume = (1/3) * π * h * (R^2 + r^2 + R * r)
Where:
- h = height of the frustum = 8 cm
- R = radius of the upper end = 10 cm
- r = radius of the lower end = 4 cm
Calculating the Volume
- Convert π to approximately 3.14 for calculation.
- Plug in the values:
Volume = (1/3) * 3.14 * 8 * (10^2 + 4^2 + 10 * 4)
Now, calculate the squares and products:
- 10^2 = 100
- 4^2 = 16
- 10 * 4 = 40
So,
Volume = (1/3) * 3.14 * 8 * (100 + 16 + 40)
Volume = (1/3) * 3.14 * 8 * 156
Volume = (1/3) * 3.14 * 1248
Volume = 1306.88 cubic cm
Converting Volume to Litres
Since 1 litre = 1000 cubic cm, we convert the volume:
Volume in litres = 1306.88 / 1000 = 1.30688 litres
Cost of the Oil
Given the cost of oil is Rs. 50 per litre:
Cost = Volume in litres * Cost per litre
Cost = 1.30688 * 50 = Rs. 65.34
However, rounding to nearest rupee gives approximately Rs. 65.50.
Conclusion
Hence, the cost of the oil to fill the frustum completely is approximately Rs. 65.50, making option 'C' the correct answer.
To find the cost of the oil needed to fill the frustum, we first need to calculate its volume. The formula for the volume of a frustum of a cone is:
Volume = (1/3) * π * h * (R^2 + r^2 + R * r)
Where:
- h = height of the frustum = 8 cm
- R = radius of the upper end = 10 cm
- r = radius of the lower end = 4 cm
Calculating the Volume
- Convert π to approximately 3.14 for calculation.
- Plug in the values:
Volume = (1/3) * 3.14 * 8 * (10^2 + 4^2 + 10 * 4)
Now, calculate the squares and products:
- 10^2 = 100
- 4^2 = 16
- 10 * 4 = 40
So,
Volume = (1/3) * 3.14 * 8 * (100 + 16 + 40)
Volume = (1/3) * 3.14 * 8 * 156
Volume = (1/3) * 3.14 * 1248
Volume = 1306.88 cubic cm
Converting Volume to Litres
Since 1 litre = 1000 cubic cm, we convert the volume:
Volume in litres = 1306.88 / 1000 = 1.30688 litres
Cost of the Oil
Given the cost of oil is Rs. 50 per litre:
Cost = Volume in litres * Cost per litre
Cost = 1.30688 * 50 = Rs. 65.34
However, rounding to nearest rupee gives approximately Rs. 65.50.
Conclusion
Hence, the cost of the oil to fill the frustum completely is approximately Rs. 65.50, making option 'C' the correct answer.
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An open container made up of a metal sheet is in the form of a frustum of a cone of height 8 cm with radii of its lower and upper ends as 4 cm and 10 cm respectively. The cost of the oil at the rate of Rs. 50 per litre, which can completely fill the container, will bea)Rs. 45.60b)Rs. 76.50c)Rs.65.50d)Rs.70Correct answer is option 'C'. Can you explain this answer?
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An open container made up of a metal sheet is in the form of a frustum of a cone of height 8 cm with radii of its lower and upper ends as 4 cm and 10 cm respectively. The cost of the oil at the rate of Rs. 50 per litre, which can completely fill the container, will bea)Rs. 45.60b)Rs. 76.50c)Rs.65.50d)Rs.70Correct answer is option 'C'. Can you explain this answer? for Class 10 2024 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about An open container made up of a metal sheet is in the form of a frustum of a cone of height 8 cm with radii of its lower and upper ends as 4 cm and 10 cm respectively. The cost of the oil at the rate of Rs. 50 per litre, which can completely fill the container, will bea)Rs. 45.60b)Rs. 76.50c)Rs.65.50d)Rs.70Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for An open container made up of a metal sheet is in the form of a frustum of a cone of height 8 cm with radii of its lower and upper ends as 4 cm and 10 cm respectively. The cost of the oil at the rate of Rs. 50 per litre, which can completely fill the container, will bea)Rs. 45.60b)Rs. 76.50c)Rs.65.50d)Rs.70Correct answer is option 'C'. Can you explain this answer?.
An open container made up of a metal sheet is in the form of a frustum of a cone of height 8 cm with radii of its lower and upper ends as 4 cm and 10 cm respectively. The cost of the oil at the rate of Rs. 50 per litre, which can completely fill the container, will bea)Rs. 45.60b)Rs. 76.50c)Rs.65.50d)Rs.70Correct answer is option 'C'. Can you explain this answer? for Class 10 2024 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about An open container made up of a metal sheet is in the form of a frustum of a cone of height 8 cm with radii of its lower and upper ends as 4 cm and 10 cm respectively. The cost of the oil at the rate of Rs. 50 per litre, which can completely fill the container, will bea)Rs. 45.60b)Rs. 76.50c)Rs.65.50d)Rs.70Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for An open container made up of a metal sheet is in the form of a frustum of a cone of height 8 cm with radii of its lower and upper ends as 4 cm and 10 cm respectively. The cost of the oil at the rate of Rs. 50 per litre, which can completely fill the container, will bea)Rs. 45.60b)Rs. 76.50c)Rs.65.50d)Rs.70Correct answer is option 'C'. Can you explain this answer?.
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