Question

Diameter of a bangle is 7 cm. Thin strip of gold is to be fixed on this bangle, find the cost (in Rs) for it at the rate of Rs.100 per 1 cm.

Answer 1

Hint: Here we have to find the total cost needed to make the stripe of gold to be fixed in the bangle. We are given the diameter so that we can easily find the circumference of the bangle. And then we can find the total cost by multiplying the circumference to the rate of fixing a thin gold strip per cm.

Complete step-by-step answer:
The diameter of the bangle is, 7 cm

So, we have our radius as, \[r = \dfrac{d}{2} = \dfrac{7}{2}\]cm.
Now, the circumference of the circle would be \[2\pi r\]
On substituting the value of r we get,
 \[ = 2 \times \pi \times \dfrac{7}{2}cm\]
On substituting the value of \[\pi = \dfrac{{22}}{7}\] , we get,
 \[ = 2 \times \dfrac{{22}}{7} \times \dfrac{7}{2}cm\]
On simplification we get,
 \[ = 22cm\]
Hence the circumference of the bangle is 22cm.
Now the rate of fixing a thin strip of gold on a bangle is, 100 per cm.
Hence, the cost of fixing a thin strip of gold on bangle is equal to circumference of bangle into the rate per cm.
Hence, the total cost \[ = Rs{\text{ (}}22 \times 100)\]
Hence the total cost is \[ = \] Rs2200.

Note: This is a general problem where we are to find mainly the circumference where we are given the diameter needed. The units are to be taken care of here when we are trying to find the circumference. And the formula also must be considered. We must convert the diameter to the radius before finding the circumference. We must not find the area instead of circumference to fix the gold strip.