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The interior of a building is in the form of a cylinder of diameter 4.3m and height 3.8, surmounted by a cone whose vertical angle is a right angle. What will be the slant height of the cone A. 4.3 m B. 4.3/2m C. 8.6m D. 8.1m Can you solve this?
Most Upvoted Answer
The interior of a building is in the form of a cylinder of diameter 4....
Solution :-
Diameter of the cylindrical portion = 4.3 m
Radius = 4.3/2 = 2.15 m
Height = 3.8 m
Lateral Surface Area of cylindrical portion = 2πeh
⇒ 2*22/7*2.15*3.8
= 359.48/7
= 51.3543 m�
It is mentioned that vertical angle of the cone is a right angle.
Let BAC be the triangle.
In Δ BAC,
Slant height 'l' = AB = AC
⇒ l� + l� = (BC)� (BC = diameter of the common base of cone and cylinder)
⇒ 2l� = (4.3)�
⇒ 2l� = 18.49
⇒ l� = 18.49/2
⇒ l� = 9.245
⇒ l = 3.04 m
So, slant height is 3.04 m
Community Answer
The interior of a building is in the form of a cylinder of diameter 4....
To find the slant height of the cone, we need to determine the height of the cone first. Let's break down the problem into two parts: the cylinder and the cone.
1. Cylinder:
- Diameter of the cylinder = 4.3 m
- Radius of the cylinder = diameter/2 = 4.3/2 = 2.15 m
- Height of the cylinder = 3.8 m
2. Cone:
- The cone is surmounted on the cylinder, so the base of the cone will have the same diameter as the cylinder, i.e., 4.3 m.
- The vertical angle of the cone is a right angle, which means that the height of the cone is equal to the radius of the cone.
- The height of the cone will be equal to the radius of the cylinder, so the height of the cone is 2.15 m.
Now, we can find the slant height of the cone using the Pythagorean theorem:
- Slant height of the cone = √(height of the cone)^2 + (radius of the cone)^2
Substituting the values:
- Slant height of the cone = √(2.15^2 + 2.15^2) = √(4.6225 + 4.6225) = √9.245 = 3.04 m
Therefore, the slant height of the cone is approximately 3.04 m.
So, the correct option is not given in the choices.
1. Cylinder:
- Diameter of the cylinder = 4.3 m
- Radius of the cylinder = diameter/2 = 4.3/2 = 2.15 m
- Height of the cylinder = 3.8 m
2. Cone:
- The cone is surmounted on the cylinder, so the base of the cone will have the same diameter as the cylinder, i.e., 4.3 m.
- The vertical angle of the cone is a right angle, which means that the height of the cone is equal to the radius of the cone.
- The height of the cone will be equal to the radius of the cylinder, so the height of the cone is 2.15 m.
Now, we can find the slant height of the cone using the Pythagorean theorem:
- Slant height of the cone = √(height of the cone)^2 + (radius of the cone)^2
Substituting the values:
- Slant height of the cone = √(2.15^2 + 2.15^2) = √(4.6225 + 4.6225) = √9.245 = 3.04 m
Therefore, the slant height of the cone is approximately 3.04 m.
So, the correct option is not given in the choices.
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The interior of a building is in the form of a cylinder of diameter 4.3m and height 3.8, surmounted by a cone whose vertical angle is a right angle. What will be the slant height of the cone A. 4.3 m B. 4.3/2m C. 8.6m D. 8.1m Can you solve this?
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The interior of a building is in the form of a cylinder of diameter 4.3m and height 3.8, surmounted by a cone whose vertical angle is a right angle. What will be the slant height of the cone A. 4.3 m B. 4.3/2m C. 8.6m D. 8.1m Can you solve this? for Class 10 2024 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about The interior of a building is in the form of a cylinder of diameter 4.3m and height 3.8, surmounted by a cone whose vertical angle is a right angle. What will be the slant height of the cone A. 4.3 m B. 4.3/2m C. 8.6m D. 8.1m Can you solve this? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The interior of a building is in the form of a cylinder of diameter 4.3m and height 3.8, surmounted by a cone whose vertical angle is a right angle. What will be the slant height of the cone A. 4.3 m B. 4.3/2m C. 8.6m D. 8.1m Can you solve this?.
The interior of a building is in the form of a cylinder of diameter 4.3m and height 3.8, surmounted by a cone whose vertical angle is a right angle. What will be the slant height of the cone A. 4.3 m B. 4.3/2m C. 8.6m D. 8.1m Can you solve this? for Class 10 2024 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about The interior of a building is in the form of a cylinder of diameter 4.3m and height 3.8, surmounted by a cone whose vertical angle is a right angle. What will be the slant height of the cone A. 4.3 m B. 4.3/2m C. 8.6m D. 8.1m Can you solve this? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The interior of a building is in the form of a cylinder of diameter 4.3m and height 3.8, surmounted by a cone whose vertical angle is a right angle. What will be the slant height of the cone A. 4.3 m B. 4.3/2m C. 8.6m D. 8.1m Can you solve this?.
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