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Find the total surface area and the volume of the conical frustum below.

 

 Jan 9, 2024
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To find the volume of this conical frustum, we can use the formula for the volume of the conical frustum which is:

 V = (1/3) x π x h x (r² + R² + (r x R))

Plugging in the values, we get:

V = (1/3) x π x 92 x (25² + 33² + (25 x 33))

V = 92/3 x π x (625 + 1089 + 825)

V = 92/3 x π x 2539

V = 92/3 x π x 2539

V = 244612.781589

V ≈ 244612.78 

 

Answer: V = 244612.78 units

 

 

 

 

To find the surface area of this conical frustum, we can use the formula for the surface area of the conical frustum which is:

SA = π x [ r²+ R² + (r + R) x √((r - R)² + h²) ]

Plugging in the values, we get:

SA = π x [ 25²+ 33² + (25 + 33) x √((25 - 33)² + 92²) ]

SA = π x [ 625 + 1089 + 58 x √(64 + 8464) ]

SA = π x [ 1714 + 58 x √8528 ]

SA = π x [ 1714 + 58 x 92.3471710449 ]

SA = π x [ 1714 + 5356.1359206 ]

SA = π x [ 7070.1359206 ]

SA  ≈ 22211.49

 

Answer: SA = 22211.49 units

 Jan 9, 2024

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