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If the radii of the circular ends of a conical bucket, which is 16cm high, are 20cm and 8cm, then find the capacity and total surface area of the bucket. [Use pi=22/7]?
Verified Answer
If the radii of the circular ends of a conical bucket, which is 16cm h...
Radius of the bigger end of the frustum (bucket) of cone = R = 20 cm 
Radius of the smaller end of the frustum (bucket) of the cone = r = 8 cm
Height = 16 cm
Volume = 1/3πh[R^2 + r^2 + R*r]
= 1/3*22/7*16[20^2 + 8^2 + 20*8]
= 352/21[400 + 64 + 160]
= (352*624)/21
= 219648/21
= 10459.43 cu cm
Now,
Slant height of the cone = l = √(R - r)^2 + h^2
l = √(20 - 8)^2 + 16^2
l = √12^2 + 16^2
l = √144 + 256
l = √400
l = 20 cm
Slant height is 20 cm
Now,
Surface area = π[R^2+ r^2 + (R + r)*l]
= 22/7[20^2 + 8^2 + (20 + 8)*16]
= 22/7[400 + 64 + 448]
= 22/7*912
= 20064/7
= 2866.29 sq cm
This question is part of UPSC exam. View all Class 10 courses
Most Upvoted Answer
If the radii of the circular ends of a conical bucket, which is 16cm h...
Given information:
- The height of the conical bucket is 16 cm.
- The radii of the circular ends of the bucket are 20 cm and 8 cm.
- The value of pi is given as 22/7.

Calculating the capacity of the bucket:
To find the capacity of the conical bucket, we need to calculate its volume.

The volume of a cone can be calculated using the formula:
Volume = (1/3) * pi * r^2 * h

Where:
- r is the radius of the circular end of the cone
- h is the height of the cone

In this case, we have two different radii for the circular ends of the bucket. To calculate the volume, we need to split the bucket into two parts: a smaller cone and a larger cone.

1. Volume of the smaller cone:
Using the formula, we can calculate the volume of the smaller cone:
Volume1 = (1/3) * (22/7) * (8^2) * 16

2. Volume of the larger cone:
Using the formula, we can calculate the volume of the larger cone:
Volume2 = (1/3) * (22/7) * (20^2) * 16

3. Total volume of the bucket:
The total volume of the bucket is the sum of the volumes of the smaller and larger cones:
Total Volume = Volume1 + Volume2

Calculating the total surface area of the bucket:
To find the total surface area of the conical bucket, we need to calculate the areas of its curved surface and circular ends.

The curved surface area of a cone can be calculated using the formula:
Curved Surface Area = pi * r * l

Where:
- r is the radius of the circular end of the cone
- l is the slant height of the cone

1. Curved surface area of the smaller cone:
To calculate the curved surface area of the smaller cone, we need to find its slant height. Using the Pythagorean theorem, we can find the slant height (l) of the smaller cone:
l1 = sqrt(h^2 + (R - r)^2)
Here, h is the height of the smaller cone, R is the radius of the larger circular end, and r is the radius of the smaller circular end.

Using the slant height, we can calculate the curved surface area of the smaller cone:
Curved Surface Area1 = (22/7) * 8 * l1

2. Curved surface area of the larger cone:
To calculate the curved surface area of the larger cone, we need to find its slant height. Using the same formula as before, we can find the slant height (l) of the larger cone:
l2 = sqrt(h^2 + (R - r)^2)
Here, h is the height of the larger cone, R is the radius of the larger circular end, and r is the radius of the smaller circular end.

Using the slant height, we can calculate the curved surface area of the larger cone:
Curved Surface Area2 = (22/7) * 20 * l2

3. Total curved surface area of the bucket:
The total curved surface area of the bucket is the sum of the curved surface areas of the smaller and larger cones:
Total
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If the radii of the circular ends of a conical bucket, which is 16cm high, are 20cm and 8cm, then find the capacity and total surface area of the bucket. [Use pi=22/7]?
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