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The diameters of the top and bottom of a bucket are 40 cm and 20 cm respectively. If the depth of the bucket is 12 cm then its volume will be
- a)8000 cm3
- b)8800 cm3
- c)9000 cm3
- d)4400 cm3
Correct answer is option 'B'. Can you explain this answer?
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Verified Answer
The diameters of the top and bottom of a bucket are 40 cm and 20 cm re...
Volume = 1/3πh(R² + r² + R*r)
= 1/3*3.14*1.2*(2² + 1² + 2*1)
= 1/3*3.14*1.2*7
= 26.376/3
Volume = 8.792 cu dm ~= 8800 cm3
Most Upvoted Answer
The diameters of the top and bottom of a bucket are 40 cm and 20 cm re...
Given: Diameter of top = 40 cm, Diameter of bottom = 20 cm and Depth = 12 cm
To find: Volume of the bucket
Formula used: Volume of frustum = 1/3πh (R² + r² + Rr)
where h = height of frustum, R = radius of bottom circle and r = radius of top circle
Explanation:
1. We need to find the radius of the top circle and radius of bottom circle using the given diameters.
Radius of top circle = Diameter/2 = 20 cm
Radius of bottom circle = Diameter/2 = 10 cm
2. Now we can substitute the given values in the formula to find the volume of frustum.
Volume of frustum = 1/3πh (R² + r² + Rr)
= 1/3π x 12 cm x (10 cm² + 20 cm² + (10 cm x 20 cm))
= 1/3π x 12 cm x (100 cm² + 400 cm² + 200 cm²)
= 1/3π x 12 cm x 700 cm²
= 2800π cm³
3. We can approximate the value of π as 22/7 to simplify the calculation.
Volume of frustum = 2800 x 22/7 cm³
= 8800 cm³
Therefore, the volume of the bucket is 8800 cm³.
Hence, option (b) 8800 cm³ is the correct answer.
To find: Volume of the bucket
Formula used: Volume of frustum = 1/3πh (R² + r² + Rr)
where h = height of frustum, R = radius of bottom circle and r = radius of top circle
Explanation:
1. We need to find the radius of the top circle and radius of bottom circle using the given diameters.
Radius of top circle = Diameter/2 = 20 cm
Radius of bottom circle = Diameter/2 = 10 cm
2. Now we can substitute the given values in the formula to find the volume of frustum.
Volume of frustum = 1/3πh (R² + r² + Rr)
= 1/3π x 12 cm x (10 cm² + 20 cm² + (10 cm x 20 cm))
= 1/3π x 12 cm x (100 cm² + 400 cm² + 200 cm²)
= 1/3π x 12 cm x 700 cm²
= 2800π cm³
3. We can approximate the value of π as 22/7 to simplify the calculation.
Volume of frustum = 2800 x 22/7 cm³
= 8800 cm³
Therefore, the volume of the bucket is 8800 cm³.
Hence, option (b) 8800 cm³ is the correct answer.
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Community Answer
The diameters of the top and bottom of a bucket are 40 cm and 20 cm re...
Given:
Diameter of top of the bucket = 40 cm
Diameter of bottom of the bucket = 20 cm
Depth of the bucket = 12 cm
To find:
Volume of the bucket
Solution:
Let us assume the height of the frustum of the bucket to be 'h'.
Then, the radius of the top of the bucket = 20 cm/2 = 10 cm.
And, the radius of the bottom of the bucket = 40 cm/2 = 20 cm.
Using the formula for the volume of frustum, we get:
Volume of bucket = 1/3 πh (r1² + r2² + r1r2)
Here, r1 = 10 cm and r2 = 20 cm
Substituting the values, we get:
Volume of bucket = 1/3 π(12) (10² + 20² + 10×20)
= 1/3 π(12) (500)
= 200 π cm³
Now, we need to find the value of 200π.
Taking π = 3.14 (approx.), we get:
Volume of bucket = 200×3.14 cm³
= 628 cm³ (approx.)
Therefore, the volume of the bucket is 628 cm³ (approx.)
Option (b) 8800 cm³ is not the correct answer.
Diameter of top of the bucket = 40 cm
Diameter of bottom of the bucket = 20 cm
Depth of the bucket = 12 cm
To find:
Volume of the bucket
Solution:
Let us assume the height of the frustum of the bucket to be 'h'.
Then, the radius of the top of the bucket = 20 cm/2 = 10 cm.
And, the radius of the bottom of the bucket = 40 cm/2 = 20 cm.
Using the formula for the volume of frustum, we get:
Volume of bucket = 1/3 πh (r1² + r2² + r1r2)
Here, r1 = 10 cm and r2 = 20 cm
Substituting the values, we get:
Volume of bucket = 1/3 π(12) (10² + 20² + 10×20)
= 1/3 π(12) (500)
= 200 π cm³
Now, we need to find the value of 200π.
Taking π = 3.14 (approx.), we get:
Volume of bucket = 200×3.14 cm³
= 628 cm³ (approx.)
Therefore, the volume of the bucket is 628 cm³ (approx.)
Option (b) 8800 cm³ is not the correct answer.
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The diameters of the top and bottom of a bucket are 40 cm and 20 cm respectively. If the depth of the bucket is 12 cm then its volume will bea)8000 cm3b)8800 cm3c)9000 cm3d)4400 cm3Correct answer is option 'B'. Can you explain this answer?
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