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A right circular cone of radius 4 cm and slant height 5 cm is curved out from a cylindrical piece of wood of same radius and height 5 cm. The surface area of the remaining wood is :
- a)84 π
- b)70 π
- c)76 π
- d)50 π
Correct answer is option 'C'. Can you explain this answer?
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A right circular cone of radius 4 cm and slant height 5 cm is curved o...
Given:
Radius of the cone (r) = 4 cm
Slant height of the cone (l) = 5 cm
Height of the cylindrical piece of wood (h) = 5 cm
Radius of the cylindrical piece of wood (R) = 4 cm
To find:
Surface area of the remaining wood
Solution:
1. Volume of the cone removed from the cylinder
The cone is carved out of the cylindrical piece of wood. So, the volume of the cone will be removed from the cylinder. Therefore, we need to find the volume of the cone.
Volume of the cone = (1/3)πr²h
= (1/3) x 22/7 x 4² x 5
= 83.33 cm³
2. Surface area of the cylindrical piece of wood
The total surface area of the cylindrical piece of wood can be found using the formula:
Total surface area of cylinder = 2πRh + 2πR²
= 2 x 22/7 x 4 x 5 + 2 x 22/7 x 4²
= 251.43 cm²
3. Surface area of the remaining wood
The surface area of the remaining wood can be found by subtracting the surface area of the carved cone from the total surface area of the cylindrical piece of wood.
Surface area of the remaining wood = Total surface area of cylinder - Surface area of carved cone
= 251.43 - (πrl)
= 251.43 - (22/7 x 4 x 5)
= 76 cm²
Therefore, the surface area of the remaining wood is 76 cm².
Hence, option (c) is the correct answer.
Radius of the cone (r) = 4 cm
Slant height of the cone (l) = 5 cm
Height of the cylindrical piece of wood (h) = 5 cm
Radius of the cylindrical piece of wood (R) = 4 cm
To find:
Surface area of the remaining wood
Solution:
1. Volume of the cone removed from the cylinder
The cone is carved out of the cylindrical piece of wood. So, the volume of the cone will be removed from the cylinder. Therefore, we need to find the volume of the cone.
Volume of the cone = (1/3)πr²h
= (1/3) x 22/7 x 4² x 5
= 83.33 cm³
2. Surface area of the cylindrical piece of wood
The total surface area of the cylindrical piece of wood can be found using the formula:
Total surface area of cylinder = 2πRh + 2πR²
= 2 x 22/7 x 4 x 5 + 2 x 22/7 x 4²
= 251.43 cm²
3. Surface area of the remaining wood
The surface area of the remaining wood can be found by subtracting the surface area of the carved cone from the total surface area of the cylindrical piece of wood.
Surface area of the remaining wood = Total surface area of cylinder - Surface area of carved cone
= 251.43 - (πrl)
= 251.43 - (22/7 x 4 x 5)
= 76 cm²
Therefore, the surface area of the remaining wood is 76 cm².
Hence, option (c) is the correct answer.
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A right circular cone of radius 4 cm and slant height 5 cm is curved o...
Answer:76π
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A right circular cone of radius 4 cm and slant height 5 cm is curved out from a cylindrical piece of wood of same radius and height 5 cm. The surface area of the remaining wood is :a)84πb)70πc)76πd)50πCorrect answer is option 'C'. Can you explain this answer?
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