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From wooden cubical block of edge 7centimetre the largest possible right conical piece is cut out whose base is one of the faces of the cube calculate the volume of the wood left in the block and the total surface area of the block left?
Most Upvoted Answer
From wooden cubical block of edge 7centimetre the largest possible rig...
Volume of block left= volume of cube- volume of cone
=a^3-1/3Πr^2h
=7×7×7-(539/12)
=298.0834cm^3
total surface area of the block left= curved surface area of cube+ curved surface area of cone- base area
=4a^2+ΠRL-Πr^2
=343+11√245/2-77/2=819.677cm^2
=a^3-1/3Πr^2h
=7×7×7-(539/12)
=298.0834cm^3
total surface area of the block left= curved surface area of cube+ curved surface area of cone- base area
=4a^2+ΠRL-Πr^2
=343+11√245/2-77/2=819.677cm^2
Community Answer
From wooden cubical block of edge 7centimetre the largest possible rig...
Given:
- Edge of the wooden cube = 7 cm
To find:
- Volume of the wood left in the block
- Total surface area of the block left
Approach:
1. Calculate the volume of the wooden cube.
2. Find the volume of the right conical piece cut out.
3. Subtract the volume of the right conical piece from the volume of the wooden cube to find the volume of the wood left.
4. Calculate the total surface area of the wooden cube.
5. Subtract the surface area of the base of the right conical piece from the total surface area of the wooden cube to find the total surface area of the block left.
Calculation:
1. Volume of the wooden cube:
- Edge of the cube = 7 cm
- Volume of a cube = (Edge)^3
- Volume of the wooden cube = (7 cm)^3 = 7 cm x 7 cm x 7 cm = 343 cm³
2. Volume of the right conical piece:
- The base of the right conical piece is one of the faces of the cube.
- Since the base is a square, the area of the base = (Edge)^2 = (7 cm)^2 = 49 cm²
- The height of the conical piece is equal to the edge of the cube, which is 7 cm.
- Volume of a cone = (1/3) x (Base area) x (Height)
- Volume of the right conical piece = (1/3) x 49 cm² x 7 cm = 49 cm² x 7 cm / 3 = 343 cm³
3. Volume of the wood left:
- Volume of the wood left = Volume of the wooden cube - Volume of the right conical piece
- Volume of the wood left = 343 cm³ - 343 cm³ = 0 cm³
4. Total surface area of the wooden cube:
- Surface area of a cube = 6 x (Edge)^2
- Total surface area of the wooden cube = 6 x (7 cm)^2 = 6 x 49 cm² = 294 cm²
5. Total surface area of the block left:
- The base of the right conical piece is removed, so the surface area of the base = 49 cm²
- Total surface area of the block left = Total surface area of the wooden cube - Surface area of the base of the right conical piece
- Total surface area of the block left = 294 cm² - 49 cm² = 245 cm²
Final Answer:
- Volume of the wood left in the block = 0 cm³
- Total surface area of the block left = 245 cm²
- Edge of the wooden cube = 7 cm
To find:
- Volume of the wood left in the block
- Total surface area of the block left
Approach:
1. Calculate the volume of the wooden cube.
2. Find the volume of the right conical piece cut out.
3. Subtract the volume of the right conical piece from the volume of the wooden cube to find the volume of the wood left.
4. Calculate the total surface area of the wooden cube.
5. Subtract the surface area of the base of the right conical piece from the total surface area of the wooden cube to find the total surface area of the block left.
Calculation:
1. Volume of the wooden cube:
- Edge of the cube = 7 cm
- Volume of a cube = (Edge)^3
- Volume of the wooden cube = (7 cm)^3 = 7 cm x 7 cm x 7 cm = 343 cm³
2. Volume of the right conical piece:
- The base of the right conical piece is one of the faces of the cube.
- Since the base is a square, the area of the base = (Edge)^2 = (7 cm)^2 = 49 cm²
- The height of the conical piece is equal to the edge of the cube, which is 7 cm.
- Volume of a cone = (1/3) x (Base area) x (Height)
- Volume of the right conical piece = (1/3) x 49 cm² x 7 cm = 49 cm² x 7 cm / 3 = 343 cm³
3. Volume of the wood left:
- Volume of the wood left = Volume of the wooden cube - Volume of the right conical piece
- Volume of the wood left = 343 cm³ - 343 cm³ = 0 cm³
4. Total surface area of the wooden cube:
- Surface area of a cube = 6 x (Edge)^2
- Total surface area of the wooden cube = 6 x (7 cm)^2 = 6 x 49 cm² = 294 cm²
5. Total surface area of the block left:
- The base of the right conical piece is removed, so the surface area of the base = 49 cm²
- Total surface area of the block left = Total surface area of the wooden cube - Surface area of the base of the right conical piece
- Total surface area of the block left = 294 cm² - 49 cm² = 245 cm²
Final Answer:
- Volume of the wood left in the block = 0 cm³
- Total surface area of the block left = 245 cm²
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From wooden cubical block of edge 7centimetre the largest possible right conical piece is cut out whose base is one of the faces of the cube calculate the volume of the wood left in the block and the total surface area of the block left?
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From wooden cubical block of edge 7centimetre the largest possible right conical piece is cut out whose base is one of the faces of the cube calculate the volume of the wood left in the block and the total surface area of the block left? 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 From wooden cubical block of edge 7centimetre the largest possible right conical piece is cut out whose base is one of the faces of the cube calculate the volume of the wood left in the block and the total surface area of the block left? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for From wooden cubical block of edge 7centimetre the largest possible right conical piece is cut out whose base is one of the faces of the cube calculate the volume of the wood left in the block and the total surface area of the block left?.
From wooden cubical block of edge 7centimetre the largest possible right conical piece is cut out whose base is one of the faces of the cube calculate the volume of the wood left in the block and the total surface area of the block left? 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 From wooden cubical block of edge 7centimetre the largest possible right conical piece is cut out whose base is one of the faces of the cube calculate the volume of the wood left in the block and the total surface area of the block left? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for From wooden cubical block of edge 7centimetre the largest possible right conical piece is cut out whose base is one of the faces of the cube calculate the volume of the wood left in the block and the total surface area of the block left?.
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