Question

T is directly proportional to the cube of r. T= 21.76 when r=4 find a formula for T in terms of r

Answer 1

Step-by-step explanation:

T is directly proportional to the cube of r. T = 21.76 when r = 4. Work out the value of T when r = 6.

Answer 2

Given,

T is directly proportional to the cube of r,

T = 21.76 when r = 4.

To find,

A formula for T in terms of r.

Solution,

It is given here, that T is directly proportional to the cube of r. This can be expressed mathematically as,

$T \propto r^3$     ...(1)

Now, when removing the proportionality sign, we use a constant of proportionality. Let this constant be 'k'. So,

$T =k \cdot r^3$     ...(2)

According to the given condition,

when r = 4,

T = 21.76.

Substituting these values in eq. (2), we can find 'k'. Thus,

$21.76 =k \cdot (4)^3$

$\implies 21.76 =64k$

$\implies k= \frac{21.76}{64}$

$\implies k=0.34$

Now, we can put this value of 'k' in eq. (2), to find the required formula. That is,

$T =0.34 r^3$

Thus the formula for T in terms of r will be T = 0.34r³.