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Two metallic right circular cones having their heights 9 cm and 18 cm and the radii of their bases 4√2 cm each have been melted together and recast into a sphere. Then Surface area of the sphere.
- a)256π
- b)100π
- c)196π
- d)144π
Correct answer is option 'D'. Can you explain this answer?
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Most Upvoted Answer
Two metallic right circular cones having their heights 9 cm and 18 cm...
To find the surface area of the sphere formed by melting and recasting the two cones, we need to follow these steps:
1. Find the volume of each cone:
- The volume of a cone can be calculated using the formula V = (1/3) * π * r^2 * h, where r is the radius and h is the height.
- For the first cone, with a height of 9 cm and a radius of 4√2 cm, the volume is V1 = (1/3) * π * (4√2)^2 * 9 = 96π cm^3.
- For the second cone, with a height of 18 cm and a radius of 4√2 cm, the volume is V2 = (1/3) * π * (4√2)^2 * 18 = 192π cm^3.
2. Find the total volume of the two cones:
- The total volume of the two cones is the sum of their individual volumes: V_total = V1 + V2 = 96π + 192π = 288π cm^3.
3. Find the radius of the sphere formed:
- The volume of a sphere can be calculated using the formula V = (4/3) * π * r^3, where r is the radius.
- Equating the volume of the sphere to the total volume of the two cones, we have: (4/3) * π * r^3 = 288π.
- Simplifying the equation, we get: r^3 = 216.
- Taking the cube root of both sides, we find: r = 6 cm.
4. Find the surface area of the sphere:
- The surface area of a sphere can be calculated using the formula A = 4 * π * r^2, where r is the radius.
- Plugging in the value of r, we have: A = 4 * π * 6^2 = 144π cm^2.
Therefore, the correct answer is option 'D', 144π.
1. Find the volume of each cone:
- The volume of a cone can be calculated using the formula V = (1/3) * π * r^2 * h, where r is the radius and h is the height.
- For the first cone, with a height of 9 cm and a radius of 4√2 cm, the volume is V1 = (1/3) * π * (4√2)^2 * 9 = 96π cm^3.
- For the second cone, with a height of 18 cm and a radius of 4√2 cm, the volume is V2 = (1/3) * π * (4√2)^2 * 18 = 192π cm^3.
2. Find the total volume of the two cones:
- The total volume of the two cones is the sum of their individual volumes: V_total = V1 + V2 = 96π + 192π = 288π cm^3.
3. Find the radius of the sphere formed:
- The volume of a sphere can be calculated using the formula V = (4/3) * π * r^3, where r is the radius.
- Equating the volume of the sphere to the total volume of the two cones, we have: (4/3) * π * r^3 = 288π.
- Simplifying the equation, we get: r^3 = 216.
- Taking the cube root of both sides, we find: r = 6 cm.
4. Find the surface area of the sphere:
- The surface area of a sphere can be calculated using the formula A = 4 * π * r^2, where r is the radius.
- Plugging in the value of r, we have: A = 4 * π * 6^2 = 144π cm^2.
Therefore, the correct answer is option 'D', 144π.
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Community Answer
Two metallic right circular cones having their heights 9 cm and 18 cm...
Volume of sphere = combined volume of the 2 cones
= 
Let the radius of sphere be r
r = 6 cm
Hence, Surface Area of the sphere = 4π x 36 = 144 π
Hence, the correct option is (d).
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Two metallic right circular cones having their heights 9 cm and 18 cm and the radii of their bases 4√2 cm each have been melted together and recast into a sphere. Then Surface area of the sphere.a)256πb)100πc)196πd)144πCorrect answer is option 'D'. Can you explain this answer?
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Two metallic right circular cones having their heights 9 cm and 18 cm and the radii of their bases 4√2 cm each have been melted together and recast into a sphere. Then Surface area of the sphere.a)256πb)100πc)196πd)144πCorrect answer is option 'D'. Can you explain this answer? for CAT 2024 is part of CAT preparation. The Question and answers have been prepared according to the CAT exam syllabus. Information about Two metallic right circular cones having their heights 9 cm and 18 cm and the radii of their bases 4√2 cm each have been melted together and recast into a sphere. Then Surface area of the sphere.a)256πb)100πc)196πd)144πCorrect answer is option 'D'. Can you explain this answer? covers all topics & solutions for CAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Two metallic right circular cones having their heights 9 cm and 18 cm and the radii of their bases 4√2 cm each have been melted together and recast into a sphere. Then Surface area of the sphere.a)256πb)100πc)196πd)144πCorrect answer is option 'D'. Can you explain this answer?.
Two metallic right circular cones having their heights 9 cm and 18 cm and the radii of their bases 4√2 cm each have been melted together and recast into a sphere. Then Surface area of the sphere.a)256πb)100πc)196πd)144πCorrect answer is option 'D'. Can you explain this answer? for CAT 2024 is part of CAT preparation. The Question and answers have been prepared according to the CAT exam syllabus. Information about Two metallic right circular cones having their heights 9 cm and 18 cm and the radii of their bases 4√2 cm each have been melted together and recast into a sphere. Then Surface area of the sphere.a)256πb)100πc)196πd)144πCorrect answer is option 'D'. Can you explain this answer? covers all topics & solutions for CAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Two metallic right circular cones having their heights 9 cm and 18 cm and the radii of their bases 4√2 cm each have been melted together and recast into a sphere. Then Surface area of the sphere.a)256πb)100πc)196πd)144πCorrect answer is option 'D'. Can you explain this answer?.
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