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The radius of base of solid cone is 9 cm and its height is 21 cm. It cut into 3 parts by two cuts, which are parallel to its base. The cuts are at height of 7 cm and 14 cm from the base respectively. What is the ratio of curved surface areas of top, middle and bottom parts respectively?
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The radius of base of solid cone is 9 cm and its height is 21 cm. It c...
Given:
To find:
Ratio of curved surface areas of top, middle and bottom parts of the cone
Solution:
To find the ratio of curved surface areas of top, middle and bottom parts of the cone, we need to first find the curved surface area of each part.
Step 1: Finding the radius and slant height of each part
- Radius of base of solid cone = 9 cm
- Height of solid cone = 21 cm
- Cuts are made at heights of 7 cm and 14 cm from the base respectively
To find:
Ratio of curved surface areas of top, middle and bottom parts of the cone
Solution:
To find the ratio of curved surface areas of top, middle and bottom parts of the cone, we need to first find the curved surface area of each part.
Step 1: Finding the radius and slant height of each part
- Bottom part: The bottom part of the cone is the part below the first cut. The height of this part is 7 cm.
- Radius of base of cone = 9 cm
- Height of cone = 21 cm
- Height of bottom part = 7 cm
To find the slant height of the bottom part, we will use Pythagoras theorem:
Slant height2 = Radius2 + Height2
Slant height2 = 92 + 72
Slant height2 = 130
Slant height = √130 ≈ 11.40 cm
Radius of bottom part = 9 cm
- Middle part: The middle part of the cone is the part between the first and second cuts. The height of this part is 7 cm.
- Radius of base of cone = 9 cm
- Height of cone = 21 cm
- Height of middle part = 14 - 7 = 7 cm
To find the radius and slant height of the middle part, we will use similar triangles:
Radius of middle part / Radius of cone = Height of middle part / Height of cone
Radius of middle part = (Radius of cone * Height of middle part) / Height of cone
Radius of middle part = (9 * 7) / 21 = 3
To find the slant height of the middle part, we will use Pythagoras theorem:
Slant height2 = Radius2 + Height2
Slant height2 = 32 + 72
Slant height2 = 58
Slant height = √58 ≈ 7.62 cm
Radius of middle part = 3 cm
- Top part: The top part of the cone is
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The radius of base of solid cone is 9 cm and its height is 21 cm. It cut into 3 parts by two cuts, which are parallel to its base. The cuts are at height of 7 cm and 14 cm from the base respectively. What is the ratio of curved surface areas of top, middle and bottom parts respectively?
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The radius of base of solid cone is 9 cm and its height is 21 cm. It cut into 3 parts by two cuts, which are parallel to its base. The cuts are at height of 7 cm and 14 cm from the base respectively. What is the ratio of curved surface areas of top, middle and bottom parts respectively? for CAT 2024 is part of CAT preparation. The Question and answers have been prepared according to the CAT exam syllabus. Information about The radius of base of solid cone is 9 cm and its height is 21 cm. It cut into 3 parts by two cuts, which are parallel to its base. The cuts are at height of 7 cm and 14 cm from the base respectively. What is the ratio of curved surface areas of top, middle and bottom parts respectively? covers all topics & solutions for CAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The radius of base of solid cone is 9 cm and its height is 21 cm. It cut into 3 parts by two cuts, which are parallel to its base. The cuts are at height of 7 cm and 14 cm from the base respectively. What is the ratio of curved surface areas of top, middle and bottom parts respectively?.
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