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The value of a coin varies directly to the square of its radius, when its thickness is constant. The radius of a coin is 1.5 cm and its value is Rs 2. What will be the radius of a coin, if its value is Rs 5?
- a)2.4 cm
- b)2.6 cm
- c)3.4 cm
- d)4.8 cm
Correct answer is option 'A'. Can you explain this answer?
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The value of a coin varies directly to the square of its radius, when ...
Given:
Radius of the coin (r1) = 1.5 cm
Value of the coin (v1) = Rs 2
We are asked to find the radius of a coin (r2) when its value (v2) is Rs 5.
To solve this problem, we can use the concept of direct variation.
Direct Variation:
In direct variation, two variables are directly proportional to each other. This means that as one variable increases, the other variable also increases in the same ratio, and vice versa.
In this case, the value of the coin is directly proportional to the square of its radius.
Mathematically, we can represent this as:
v ∝ r^2
Using this equation, we can write the proportionality constant as:
v = k*r^2
where k is the constant of variation.
Finding the constant of variation (k):
We can find the constant of variation (k) by substituting the given values of radius and value of the coin.
v1 = k*r1^2
2 = k*(1.5)^2
2 = k*2.25
Solving for k, we get:
k = 2/2.25
k = 8/9
Now, we can use this value of k to find the radius of the coin when its value is Rs 5.
Finding the radius when the value is Rs 5:
Using the equation v = k*r^2, we can substitute the values of v2 and k.
v2 = k*r2^2
5 = (8/9)*(r2)^2
5*(9/8) = r2^2
45/8 = r2^2
Taking the square root on both sides, we get:
sqrt(45/8) = r2
Simplifying, we get:
r2 = sqrt(45/8)
r2 = sqrt(45)/sqrt(8)
r2 = (3*sqrt(5))/sqrt(8)
r2 = (3*sqrt(5))/(2*sqrt(2))
r2 = (3/2)*(sqrt(5)/sqrt(2))
r2 = (3/2)*(sqrt(5)*sqrt(2))/(sqrt(2)*sqrt(2))
r2 = (3/2)*(sqrt(10))/(sqrt(2))
r2 = (3*sqrt(10))/(2*sqrt(2))
r2 = (3/2)*(sqrt(10)/sqrt(2))
r2 = (3/2)*(sqrt(10)/2)
r2 = (3/4)*sqrt(10)
Approximating, we get:
r2 ≈ 2.4 cm
Therefore, the radius of the coin when its value is Rs 5 is approximately 2.4 cm.
Radius of the coin (r1) = 1.5 cm
Value of the coin (v1) = Rs 2
We are asked to find the radius of a coin (r2) when its value (v2) is Rs 5.
To solve this problem, we can use the concept of direct variation.
Direct Variation:
In direct variation, two variables are directly proportional to each other. This means that as one variable increases, the other variable also increases in the same ratio, and vice versa.
In this case, the value of the coin is directly proportional to the square of its radius.
Mathematically, we can represent this as:
v ∝ r^2
Using this equation, we can write the proportionality constant as:
v = k*r^2
where k is the constant of variation.
Finding the constant of variation (k):
We can find the constant of variation (k) by substituting the given values of radius and value of the coin.
v1 = k*r1^2
2 = k*(1.5)^2
2 = k*2.25
Solving for k, we get:
k = 2/2.25
k = 8/9
Now, we can use this value of k to find the radius of the coin when its value is Rs 5.
Finding the radius when the value is Rs 5:
Using the equation v = k*r^2, we can substitute the values of v2 and k.
v2 = k*r2^2
5 = (8/9)*(r2)^2
5*(9/8) = r2^2
45/8 = r2^2
Taking the square root on both sides, we get:
sqrt(45/8) = r2
Simplifying, we get:
r2 = sqrt(45/8)
r2 = sqrt(45)/sqrt(8)
r2 = (3*sqrt(5))/sqrt(8)
r2 = (3*sqrt(5))/(2*sqrt(2))
r2 = (3/2)*(sqrt(5)/sqrt(2))
r2 = (3/2)*(sqrt(5)*sqrt(2))/(sqrt(2)*sqrt(2))
r2 = (3/2)*(sqrt(10))/(sqrt(2))
r2 = (3*sqrt(10))/(2*sqrt(2))
r2 = (3/2)*(sqrt(10)/sqrt(2))
r2 = (3/2)*(sqrt(10)/2)
r2 = (3/4)*sqrt(10)
Approximating, we get:
r2 ≈ 2.4 cm
Therefore, the radius of the coin when its value is Rs 5 is approximately 2.4 cm.
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The value of a coin varies directly to the square of its radius, when its thickness is constant. The radius of a coin is 1.5 cm and its value is Rs 2. What will be the radius of a coin, if its value is Rs 5?a)2.4 cmb)2.6 cmc)3.4 cmd)4.8 cmCorrect answer is option 'A'. Can you explain this answer?
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