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A hit-me doll is in the shape of a hemisphere at the base, a cylinder as the body and a right circular cone as its head, such that the base of the cone rests on the cylinder. The total height of the doll is 80 cm, the diameter of the hemispherical base is 10 cm, and the slant height of the conical top is 13 cm. What is the total surface area of the doll?
  • a)
    745 π sq. cm
  • b)
    500 π sq. c m
  • c)
    695π sq. cm
  • d)
    580 π sq. cm
Correct answer is option 'A'. Can you explain this answer?
Verified Answer
A hit-me doll is in the shape of a hemisphere at the base, a cylinder ...
Surface area of the doll = Surface area of the hemispherical section + Surface area of the cylindrical section + Surface area of the conical section
= 2πr2 + 2πrH + πrl 
(Where H is the height of the cylindrical section and / is the slant height of the conical section. Also, radius of all the three sections will be the same since they have the same base.)
r = 5 cm
Slant height of the conical section = 13 cm
Therefore, height of the conical section

= 12 cm
The hemispherical portion also contributes to the total height of the doll since the height of the hemispherical section will be its radius itself.
Therefore, height of the cylindrical section = total height of the doll - (height of the conical section + radius of the hemispherical portion)
= 80 - (12 + 5)
= 63 cm
Therefore, surface area of the hit-me doll
= 2 x π x 52 + 2 x π x 5 x 63 + π x 5 x 13
= π x (2 x 25 + 2 x 5 x 63 + 5 x 13)
= 7 45π sq. cm
Hence, option 1.
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A hit-me doll is in the shape of a hemisphere at the base, a cylinder as the body and a right circular cone as its head, such that the base of the cone rests on the cylinder. The total height of the doll is 80 cm, the diameter of the hemispherical base is 10 cm, and the slant height of the conical top is 13 cm. What is the total surface area of the doll?a)745 sq. cmb)500 sq. c mc)695 sq. cmd)580 sq. cmCorrect answer is option 'A'. Can you explain this answer?
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A hit-me doll is in the shape of a hemisphere at the base, a cylinder as the body and a right circular cone as its head, such that the base of the cone rests on the cylinder. The total height of the doll is 80 cm, the diameter of the hemispherical base is 10 cm, and the slant height of the conical top is 13 cm. What is the total surface area of the doll?a)745 sq. cmb)500 sq. c mc)695 sq. cmd)580 sq. cmCorrect answer is option 'A'. 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 A hit-me doll is in the shape of a hemisphere at the base, a cylinder as the body and a right circular cone as its head, such that the base of the cone rests on the cylinder. The total height of the doll is 80 cm, the diameter of the hemispherical base is 10 cm, and the slant height of the conical top is 13 cm. What is the total surface area of the doll?a)745 sq. cmb)500 sq. c mc)695 sq. cmd)580 sq. cmCorrect answer is option 'A'. Can you explain this answer? covers all topics & solutions for CAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A hit-me doll is in the shape of a hemisphere at the base, a cylinder as the body and a right circular cone as its head, such that the base of the cone rests on the cylinder. The total height of the doll is 80 cm, the diameter of the hemispherical base is 10 cm, and the slant height of the conical top is 13 cm. What is the total surface area of the doll?a)745 sq. cmb)500 sq. c mc)695 sq. cmd)580 sq. cmCorrect answer is option 'A'. Can you explain this answer?.
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