Answer
Verified
478.5k+ views
Hint: When a variable varies directly to another (say x varies directly as y), we can write the relation as x=ky (where k is a proportional constant). In this case, since r varies directly as the cube of s, we can write the relation as r=k${{s}^{3}}$ and then solve the question.
Complete step-by-step answer:
Firstly, we try to use the first condition given in the problem (that is, r=5 when s=3). This would help us in finding the value of proportional constant.
r=k${{s}^{3}}$
Putting the value of r=5 when s=3, we get,
5=k$\times {{3}^{3}}$
5=27k
k=$\dfrac{5}{27}$ -- (1)
Now, since we have the value of proportional constant, we can find the value of r for any value of s. We now just have to put the value of k and s in equation r=k${{s}^{3}}$ to get the value of r. Now, we find the value of r for s=2.
r=k${{s}^{3}}$
r=$\dfrac{5}{27}$$\times {{2}^{3}}$
r=$\dfrac{5\times 8}{27}$
r=$\dfrac{40}{27}$
Thus, the value of r is $\dfrac{40}{27}$. Hence, the correct option is (d) None of these.
Hint: To solve problems involving direct and inverse variations in general, we use a general principle to solve the problems. Suppose, c varies directly with d and inversely with e. We use the following relation- c=k$\dfrac{d}{e}$(where k is the value of proportionality constant). The problem can then be solved by acquiring any additional relation which would further help in evaluating the problem further.
Complete step-by-step answer:
Firstly, we try to use the first condition given in the problem (that is, r=5 when s=3). This would help us in finding the value of proportional constant.
r=k${{s}^{3}}$
Putting the value of r=5 when s=3, we get,
5=k$\times {{3}^{3}}$
5=27k
k=$\dfrac{5}{27}$ -- (1)
Now, since we have the value of proportional constant, we can find the value of r for any value of s. We now just have to put the value of k and s in equation r=k${{s}^{3}}$ to get the value of r. Now, we find the value of r for s=2.
r=k${{s}^{3}}$
r=$\dfrac{5}{27}$$\times {{2}^{3}}$
r=$\dfrac{5\times 8}{27}$
r=$\dfrac{40}{27}$
Thus, the value of r is $\dfrac{40}{27}$. Hence, the correct option is (d) None of these.
Hint: To solve problems involving direct and inverse variations in general, we use a general principle to solve the problems. Suppose, c varies directly with d and inversely with e. We use the following relation- c=k$\dfrac{d}{e}$(where k is the value of proportionality constant). The problem can then be solved by acquiring any additional relation which would further help in evaluating the problem further.
Recently Updated Pages
Change the following sentences into negative and interrogative class 10 english CBSE
A Paragraph on Pollution in about 100-150 Words
One cusec is equal to how many liters class 8 maths CBSE
The Equation xxx + 2 is Satisfied when x is Equal to Class 10 Maths
What were the social economic and political conditions class 10 social science CBSE
Write a letter to the principal requesting him to grant class 10 english CBSE
Trending doubts
The Equation xxx + 2 is Satisfied when x is Equal to Class 10 Maths
In Indian rupees 1 trillion is equal to how many c class 8 maths CBSE
How do you graph the function fx 4x class 9 maths CBSE
Why is there a time difference of about 5 hours between class 10 social science CBSE
Change the following sentences into negative and interrogative class 10 english CBSE
Write a letter to the principal requesting him to grant class 10 english CBSE
What is the past participle of wear Is it worn or class 10 english CBSE
Why did the British treat the Muslims harshly immediately class 10 social science CBSE
A Paragraph on Pollution in about 100-150 Words