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The area of a cylinder varies jointly with the radius and the height. When the radius is 3 and the height is 6, the area is 367E. Find the area when the radius is 4 and the height is 5.
- a)40π
- b)32π
- c)36π
- d)48π
Correct answer is option 'A'. Can you explain this answer?
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Verified Answer
The area of a cylinder varies jointly with the radius and the height. ...
Let A be the area, r be the radius and h be the height.
A = krh
When r = 3 and h = 6,A = 36π
36π = k x 3 x 6
k = 2π
When r = 4 and h = 5
A = 2πx 4 x 5 = 40π
Hence, option 1.
A = krh
When r = 3 and h = 6,A = 36π
36π = k x 3 x 6
k = 2π
When r = 4 and h = 5
A = 2πx 4 x 5 = 40π
Hence, option 1.
Most Upvoted Answer
The area of a cylinder varies jointly with the radius and the height. ...
To solve this problem, we will use the concept of joint variation. Joint variation is a type of direct variation where a variable depends on the product of two or more other variables. In this case, the area of the cylinder depends on both the radius and the height.
Let's denote the area of the cylinder as A, the radius as r, and the height as h. According to the problem, the area of the cylinder varies jointly with the radius and the height. This can be represented mathematically as:
A ∝ r * h
We can also write this equation in the form of a proportion:
A = k * r * h
where k is the constant of variation. We can find the value of k by using the given information. When the radius is 3 and the height is 6, the area is 367E. Substituting these values into the equation, we have:
367E = k * 3 * 6
Simplifying the equation, we get:
367E = 18k
Now, we need to find the value of k. To do this, we divide both sides of the equation by 18:
k = 367E / 18
k = 20.39E
Now that we have the value of k, we can use it to find the area when the radius is 4 and the height is 5. Substituting these values into the equation, we have:
A = 20.39E * 4 * 5
Simplifying the equation, we get:
A = 407.8E
Therefore, the area of the cylinder when the radius is 4 and the height is 5 is 407.8E. However, this answer is not among the options provided. Let's check our calculations.
Calculating the area using the given options:
- Option A: 40
- Option B: 32
- Option C: 36
- Option D: 48
None of these options match our calculation of 407.8E. Therefore, none of the given options is correct. It is possible that there was an error in the options provided or in the given answer. Please double-check the question and the answer choices to ensure accuracy.
Let's denote the area of the cylinder as A, the radius as r, and the height as h. According to the problem, the area of the cylinder varies jointly with the radius and the height. This can be represented mathematically as:
A ∝ r * h
We can also write this equation in the form of a proportion:
A = k * r * h
where k is the constant of variation. We can find the value of k by using the given information. When the radius is 3 and the height is 6, the area is 367E. Substituting these values into the equation, we have:
367E = k * 3 * 6
Simplifying the equation, we get:
367E = 18k
Now, we need to find the value of k. To do this, we divide both sides of the equation by 18:
k = 367E / 18
k = 20.39E
Now that we have the value of k, we can use it to find the area when the radius is 4 and the height is 5. Substituting these values into the equation, we have:
A = 20.39E * 4 * 5
Simplifying the equation, we get:
A = 407.8E
Therefore, the area of the cylinder when the radius is 4 and the height is 5 is 407.8E. However, this answer is not among the options provided. Let's check our calculations.
Calculating the area using the given options:
- Option A: 40
- Option B: 32
- Option C: 36
- Option D: 48
None of these options match our calculation of 407.8E. Therefore, none of the given options is correct. It is possible that there was an error in the options provided or in the given answer. Please double-check the question and the answer choices to ensure accuracy.
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The area of a cylinder varies jointly with the radius and the height. When the radius is 3 and the height is 6, the area is 367E. Find the area when the radius is 4 and the height is 5.a)40πb)32πc)36πd)48πCorrect answer is option 'A'. Can you explain this answer?
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