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Read the following information carefully and answer the questions based on it.
Four surfaces- a cube, a cuboid, a cylinder and a sphere are in consideration. The length of the cube is (2x-8) cm while its lateral surface area is 4(yz-4y) sq cm. The length and breadth of the cuboid is (x+y) cm and (y+z) cm respectively. Volume of the cuboid is (5xyz-688) cubic cm. The radius of the cylinder is x cm and its height is (z-3) cm. If it’s dimensions were reversed, the volume of the cylinder will become 3/2 times of its original volume. The radius of the sphere is (y+1) cm. If it was melted into smaller spheres of radius (x/2) cm, the number of spheres that would be formed is 27. The radius of both the smaller and larger spheres is more than 5 cm.
Q. What is the length of the rod of maximum length that can be inserted into the cube without disturbing its dimensions?
- a)20√3 cm
- b)24√3 cm
- c)18√3 cm
- d)15√3 cm
- e)None of these
Correct answer is option 'A'. Can you explain this answer?
Most Upvoted Answer
Read the following information carefully and answer the questions bas...
Length of the cube = 2x - 8
⇒ Lateral surface area of the cube = 4a2 = 4(2x - 8)2 = 4(4x2 + 64 - 32x)
⇒ 4(4x2 + 64 - 32x) = 4y (z - 4) ---------- (1)
Radius of cylinder = x
Height of cylinder = (z - 3)
Volume of the cylinder = π * x2 *(z - 3)
If the dimensions were reversed = π*(z - 3)2*x
Thus, π*(z - 3)2*x = 3/2* π*x2*(z - 3)
⇒ z - 3 = 3/2*x
⇒ z = (3x/2) + 3
Now, radius of sphere = y + 1 cm
Volume of sphere = 4π/3*(y + 1)3
Radius of smaller sphere = x/2
Volume of smaller sphere = 4π/3*(x/2)3
⇒ 4π/3*(y + 1)3 = 27*4 π/3*(x/2)3
⇒ y + 1 = 3(x/2) = 3x/2
⇒ y = (3x/2) -1
From equation (1) we get
4(4x2 + 64-32x) = 4y (z - 4) = 4(3x/2 - 1)(3x/2 + 3 - 4) = (3x - 2)2
⇒ 16x2 + 256 - 128x = 9x2 + 4 - 12x
⇒ 7x2 - 116x + 252 = 0
⇒ (x - 14)(7x - 18) = 0
⇒ x = 14 or x = 18/7
So, z = 3x/2+3 = 24 or 48/7
And, y = 3x/2-1 = 20 or 20/7. But y + 1 = 27/7< />
Thus, y = 20, x = 14 and z = 24
Now, length of cuboid = x + y = 14 + 20 = 34 cm
Breadth of cuboid = y + z = 20 + 24 = 44 cm
Volume of cuboid = 5xyz - 688 = 5*14*20*24 - 688 = 32912 cubic cm
Height of cuboid = 32912/34/44 = 22cm
Thus,
For cube, edge = 2x - 8 = 2*14 - 8 = 20 cm
For cuboid, length = 34 cm, breadth = 44 cm, heigh t= 22 cm
For cylinder, radius=14 cm, height = 24 - 3 = 21 cm
For smaller sphere, radius = 7 cm
For larger sphere, radius = 21 cm
Length of rod of maximum length that can be inserted = √3*edge length = 20√3 cm
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Read the following information carefully and answer the questions based on it.Four surfaces- a cube, a cuboid, a cylinder and a sphere are in consideration. The length of the cube is (2x-8) cm while its lateral surface area is 4(yz-4y) sq cm. The length and breadth of the cuboid is (x+y) cm and (y+z) cm respectively. Volume of the cuboid is (5xyz-688) cubic cm. The radius of the cylinder is x cm and its height is (z-3) cm. If it’s dimensions were reversed, the volume of the cylinder will become 3/2 times of its original volume. The radius of the sphere is (y+1) cm. If it was melted into smaller spheres of radius (x/2) cm, the number of spheres that would be formed is 27. The radius of both the smaller and larger spheres is more than 5 cm.Q. What is the length of the rod of maximum length that can be inserted into the cube without disturbing its dimensions?a)20√3 cmb)24√3 cmc)18√3 cmd)15√3 cme)None of theseCorrect answer is option 'A'. Can you explain this answer?
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Read the following information carefully and answer the questions based on it.Four surfaces- a cube, a cuboid, a cylinder and a sphere are in consideration. The length of the cube is (2x-8) cm while its lateral surface area is 4(yz-4y) sq cm. The length and breadth of the cuboid is (x+y) cm and (y+z) cm respectively. Volume of the cuboid is (5xyz-688) cubic cm. The radius of the cylinder is x cm and its height is (z-3) cm. If it’s dimensions were reversed, the volume of the cylinder will become 3/2 times of its original volume. The radius of the sphere is (y+1) cm. If it was melted into smaller spheres of radius (x/2) cm, the number of spheres that would be formed is 27. The radius of both the smaller and larger spheres is more than 5 cm.Q. What is the length of the rod of maximum length that can be inserted into the cube without disturbing its dimensions?a)20√3 cmb)24√3 cmc)18√3 cmd)15√3 cme)None of theseCorrect answer is option 'A'. Can you explain this answer? for Banking Exams 2025 is part of Banking Exams preparation. The Question and answers have been prepared according to the Banking Exams exam syllabus. Information about Read the following information carefully and answer the questions based on it.Four surfaces- a cube, a cuboid, a cylinder and a sphere are in consideration. The length of the cube is (2x-8) cm while its lateral surface area is 4(yz-4y) sq cm. The length and breadth of the cuboid is (x+y) cm and (y+z) cm respectively. Volume of the cuboid is (5xyz-688) cubic cm. The radius of the cylinder is x cm and its height is (z-3) cm. If it’s dimensions were reversed, the volume of the cylinder will become 3/2 times of its original volume. The radius of the sphere is (y+1) cm. If it was melted into smaller spheres of radius (x/2) cm, the number of spheres that would be formed is 27. The radius of both the smaller and larger spheres is more than 5 cm.Q. What is the length of the rod of maximum length that can be inserted into the cube without disturbing its dimensions?a)20√3 cmb)24√3 cmc)18√3 cmd)15√3 cme)None of theseCorrect answer is option 'A'. Can you explain this answer? covers all topics & solutions for Banking Exams 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Read the following information carefully and answer the questions based on it.Four surfaces- a cube, a cuboid, a cylinder and a sphere are in consideration. The length of the cube is (2x-8) cm while its lateral surface area is 4(yz-4y) sq cm. The length and breadth of the cuboid is (x+y) cm and (y+z) cm respectively. Volume of the cuboid is (5xyz-688) cubic cm. The radius of the cylinder is x cm and its height is (z-3) cm. If it’s dimensions were reversed, the volume of the cylinder will become 3/2 times of its original volume. The radius of the sphere is (y+1) cm. If it was melted into smaller spheres of radius (x/2) cm, the number of spheres that would be formed is 27. The radius of both the smaller and larger spheres is more than 5 cm.Q. What is the length of the rod of maximum length that can be inserted into the cube without disturbing its dimensions?a)20√3 cmb)24√3 cmc)18√3 cmd)15√3 cme)None of theseCorrect answer is option 'A'. Can you explain this answer?.
Read the following information carefully and answer the questions based on it.Four surfaces- a cube, a cuboid, a cylinder and a sphere are in consideration. The length of the cube is (2x-8) cm while its lateral surface area is 4(yz-4y) sq cm. The length and breadth of the cuboid is (x+y) cm and (y+z) cm respectively. Volume of the cuboid is (5xyz-688) cubic cm. The radius of the cylinder is x cm and its height is (z-3) cm. If it’s dimensions were reversed, the volume of the cylinder will become 3/2 times of its original volume. The radius of the sphere is (y+1) cm. If it was melted into smaller spheres of radius (x/2) cm, the number of spheres that would be formed is 27. The radius of both the smaller and larger spheres is more than 5 cm.Q. What is the length of the rod of maximum length that can be inserted into the cube without disturbing its dimensions?a)20√3 cmb)24√3 cmc)18√3 cmd)15√3 cme)None of theseCorrect answer is option 'A'. Can you explain this answer? for Banking Exams 2025 is part of Banking Exams preparation. The Question and answers have been prepared according to the Banking Exams exam syllabus. Information about Read the following information carefully and answer the questions based on it.Four surfaces- a cube, a cuboid, a cylinder and a sphere are in consideration. The length of the cube is (2x-8) cm while its lateral surface area is 4(yz-4y) sq cm. The length and breadth of the cuboid is (x+y) cm and (y+z) cm respectively. Volume of the cuboid is (5xyz-688) cubic cm. The radius of the cylinder is x cm and its height is (z-3) cm. If it’s dimensions were reversed, the volume of the cylinder will become 3/2 times of its original volume. The radius of the sphere is (y+1) cm. If it was melted into smaller spheres of radius (x/2) cm, the number of spheres that would be formed is 27. The radius of both the smaller and larger spheres is more than 5 cm.Q. What is the length of the rod of maximum length that can be inserted into the cube without disturbing its dimensions?a)20√3 cmb)24√3 cmc)18√3 cmd)15√3 cme)None of theseCorrect answer is option 'A'. Can you explain this answer? covers all topics & solutions for Banking Exams 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Read the following information carefully and answer the questions based on it.Four surfaces- a cube, a cuboid, a cylinder and a sphere are in consideration. The length of the cube is (2x-8) cm while its lateral surface area is 4(yz-4y) sq cm. The length and breadth of the cuboid is (x+y) cm and (y+z) cm respectively. Volume of the cuboid is (5xyz-688) cubic cm. The radius of the cylinder is x cm and its height is (z-3) cm. If it’s dimensions were reversed, the volume of the cylinder will become 3/2 times of its original volume. The radius of the sphere is (y+1) cm. If it was melted into smaller spheres of radius (x/2) cm, the number of spheres that would be formed is 27. The radius of both the smaller and larger spheres is more than 5 cm.Q. What is the length of the rod of maximum length that can be inserted into the cube without disturbing its dimensions?a)20√3 cmb)24√3 cmc)18√3 cmd)15√3 cme)None of theseCorrect answer is option 'A'. Can you explain this answer?.
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