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A reservoir is in the shape of frustum of a type circular cone. it is 8 m across at the top and 4 m across at the bottom. if it is 6 m Deep, then its capacity is?
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A reservoir is in the shape of frustum of a type circular cone. it is ...
To find the capacity of the reservoir shaped like a frustum of a cone, we can use the formula for the volume of a frustum. The formula is given by:
Volume (V) = (1/3) * π * h * (R^2 + r^2 + R * r)
Where:
- h = height of the frustum
- R = radius of the top base
- r = radius of the bottom base
Let’s break down the calculation.
Step 1: Dimensions of the Frustum
- Diameter at the top: 8 m
- Radius (R) = 8/2 = 4 m
- Diameter at the bottom: 4 m
- Radius (r) = 4/2 = 2 m
- Height (h): 6 m
Step 2: Volume Calculation
- Substituting values into the formula:
- V = (1/3) * π * 6 * (4^2 + 2^2 + 4 * 2)
- V = (1/3) * π * 6 * (16 + 4 + 8)
- V = (1/3) * π * 6 * 28
- V = (1/3) * π * 168
- V = 56π
Step 3: Final Volume in Cubic Meters
- Using π ≈ 3.14:
- V ≈ 56 * 3.14
- V ≈ 175.84 m³
Thus, the capacity of the reservoir is approximately 175.84 cubic meters. This volume represents the amount of water the reservoir can hold when completely filled.
Volume (V) = (1/3) * π * h * (R^2 + r^2 + R * r)
Where:
- h = height of the frustum
- R = radius of the top base
- r = radius of the bottom base
Let’s break down the calculation.
Step 1: Dimensions of the Frustum
- Diameter at the top: 8 m
- Radius (R) = 8/2 = 4 m
- Diameter at the bottom: 4 m
- Radius (r) = 4/2 = 2 m
- Height (h): 6 m
Step 2: Volume Calculation
- Substituting values into the formula:
- V = (1/3) * π * 6 * (4^2 + 2^2 + 4 * 2)
- V = (1/3) * π * 6 * (16 + 4 + 8)
- V = (1/3) * π * 6 * 28
- V = (1/3) * π * 168
- V = 56π
Step 3: Final Volume in Cubic Meters
- Using π ≈ 3.14:
- V ≈ 56 * 3.14
- V ≈ 175.84 m³
Thus, the capacity of the reservoir is approximately 175.84 cubic meters. This volume represents the amount of water the reservoir can hold when completely filled.
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A reservoir is in the shape of frustum of a type circular cone. it is 8 m across at the top and 4 m across at the bottom. if it is 6 m Deep, then its capacity is?
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A reservoir is in the shape of frustum of a type circular cone. it is 8 m across at the top and 4 m across at the bottom. if it is 6 m Deep, then its capacity is? 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 A reservoir is in the shape of frustum of a type circular cone. it is 8 m across at the top and 4 m across at the bottom. if it is 6 m Deep, then its capacity is? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A reservoir is in the shape of frustum of a type circular cone. it is 8 m across at the top and 4 m across at the bottom. if it is 6 m Deep, then its capacity is?.
A reservoir is in the shape of frustum of a type circular cone. it is 8 m across at the top and 4 m across at the bottom. if it is 6 m Deep, then its capacity is? 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 A reservoir is in the shape of frustum of a type circular cone. it is 8 m across at the top and 4 m across at the bottom. if it is 6 m Deep, then its capacity is? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A reservoir is in the shape of frustum of a type circular cone. it is 8 m across at the top and 4 m across at the bottom. if it is 6 m Deep, then its capacity is?.
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