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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. Which of the following surfaces have maximum total surface area?
- a)A cube with lateral surface area equal to xy+3x+z2 +12y+62 sq cm
- b)A hemisphere of radius (x+y+z+5)/3 cm
- c)A cone of radius y2/(2x-12) cm and height z+1 cm
- d)A cylinder with radius 3x-z cm and volume z3+y3-440 cubic cm
- e)None of these
Correct answer is option 'C'. Can you explain this answer?
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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
For A, we have
Lateral surface area of the surface = xy + 3x + z2 + 12y + 62
= 14*20 + 3*14 + 242 + 12*20 + 62 =1200
⇒ 4*area of base = 1200
⇒ Area of base = 300 sq cm
⇒ Total surface area of the cube=6*area of base=6*300=1800 sq cm
For B, we have
Radius of hemisphere = (x+y+z+5)/3= (14+20+24+5)/3 = 21 cm
Total surface area of the hemisphere=3 π*21*21 = 4158 sq cm
For C, we have
Radius of the cone= y2/(2x-12)=20*20/(28-12) = 25 cm
Height of the cone = z + 1 = 25 cm
⇒ Slant height of the cone=√(252 +252) = 25√2 cm
Total Surface area of the cone = π*radius2 + π*radius*slant height = π*252+ π*25*25√2 = 1964.28+2777.919 = 4742.204 sq cm
For D, we have
Radius of cylinder = 3x - z = 3*14 - 24 = 18 cm
Volume of the cylinder = z3 + y3 - 440 = 243 + 203 - 440 = 21384 cubic cm
Area of base = π*18*18 = 324 π sq cm
Height of the cylinder = Volume of the cylinder/Area of base = 21384/324 π = 21 cm
⇒ Total surface area of the cylinder = 2*area of base +2 π*radius*height = 2 π*182 + 2 π*18*21 = 2036.57 + 2376 = 4412.57 sq cm
Thus, total surface area of the cone is maximum
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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. Which of the following surfaces have maximum total surface area?a)A cube with lateral surface area equal to xy+3x+z2 +12y+62 sq cmb)A hemisphere of radius (x+y+z+5)/3 cmc)A cone of radius y2/(2x-12) cm and height z+1 cmd)A cylinder with radius 3x-z cm and volume z3+y3-440 cubic cme)None of theseCorrect answer is option 'C'. 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. Which of the following surfaces have maximum total surface area?a)A cube with lateral surface area equal to xy+3x+z2 +12y+62 sq cmb)A hemisphere of radius (x+y+z+5)/3 cmc)A cone of radius y2/(2x-12) cm and height z+1 cmd)A cylinder with radius 3x-z cm and volume z3+y3-440 cubic cme)None of theseCorrect answer is option 'C'. 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. Which of the following surfaces have maximum total surface area?a)A cube with lateral surface area equal to xy+3x+z2 +12y+62 sq cmb)A hemisphere of radius (x+y+z+5)/3 cmc)A cone of radius y2/(2x-12) cm and height z+1 cmd)A cylinder with radius 3x-z cm and volume z3+y3-440 cubic cme)None of theseCorrect answer is option 'C'. 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. Which of the following surfaces have maximum total surface area?a)A cube with lateral surface area equal to xy+3x+z2 +12y+62 sq cmb)A hemisphere of radius (x+y+z+5)/3 cmc)A cone of radius y2/(2x-12) cm and height z+1 cmd)A cylinder with radius 3x-z cm and volume z3+y3-440 cubic cme)None of theseCorrect answer is option 'C'. 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. Which of the following surfaces have maximum total surface area?a)A cube with lateral surface area equal to xy+3x+z2 +12y+62 sq cmb)A hemisphere of radius (x+y+z+5)/3 cmc)A cone of radius y2/(2x-12) cm and height z+1 cmd)A cylinder with radius 3x-z cm and volume z3+y3-440 cubic cme)None of theseCorrect answer is option 'C'. 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. Which of the following surfaces have maximum total surface area?a)A cube with lateral surface area equal to xy+3x+z2 +12y+62 sq cmb)A hemisphere of radius (x+y+z+5)/3 cmc)A cone of radius y2/(2x-12) cm and height z+1 cmd)A cylinder with radius 3x-z cm and volume z3+y3-440 cubic cme)None of theseCorrect answer is option 'C'. 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. Which of the following surfaces have maximum total surface area?a)A cube with lateral surface area equal to xy+3x+z2 +12y+62 sq cmb)A hemisphere of radius (x+y+z+5)/3 cmc)A cone of radius y2/(2x-12) cm and height z+1 cmd)A cylinder with radius 3x-z cm and volume z3+y3-440 cubic cme)None of theseCorrect answer is option 'C'. 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. Which of the following surfaces have maximum total surface area?a)A cube with lateral surface area equal to xy+3x+z2 +12y+62 sq cmb)A hemisphere of radius (x+y+z+5)/3 cmc)A cone of radius y2/(2x-12) cm and height z+1 cmd)A cylinder with radius 3x-z cm and volume z3+y3-440 cubic cme)None of theseCorrect answer is option 'C'. Can you explain this answer?, a detailed solution 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. Which of the following surfaces have maximum total surface area?a)A cube with lateral surface area equal to xy+3x+z2 +12y+62 sq cmb)A hemisphere of radius (x+y+z+5)/3 cmc)A cone of radius y2/(2x-12) cm and height z+1 cmd)A cylinder with radius 3x-z cm and volume z3+y3-440 cubic cme)None of theseCorrect answer is option 'C'. Can you explain this answer? has been provided alongside types of 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. Which of the following surfaces have maximum total surface area?a)A cube with lateral surface area equal to xy+3x+z2 +12y+62 sq cmb)A hemisphere of radius (x+y+z+5)/3 cmc)A cone of radius y2/(2x-12) cm and height z+1 cmd)A cylinder with radius 3x-z cm and volume z3+y3-440 cubic cme)None of theseCorrect answer is option 'C'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice 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. Which of the following surfaces have maximum total surface area?a)A cube with lateral surface area equal to xy+3x+z2 +12y+62 sq cmb)A hemisphere of radius (x+y+z+5)/3 cmc)A cone of radius y2/(2x-12) cm and height z+1 cmd)A cylinder with radius 3x-z cm and volume z3+y3-440 cubic cme)None of theseCorrect answer is option 'C'. Can you explain this answer? tests, examples and also practice Banking Exams tests.
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