The outer edge of a circular running track is 330 m long. If it is widened by 7m around find the cost of widening it at rupees8 per m2.
Answers
Answer:
₹19712
Step-by-step explanation:
Given: A circle of circumference 330 m, widened by 7 m to make a track whose cost of widening is 8₹/m².
Solution: Now let the circle with circumference 330 m be named A, and a new circle is formed by widening it by 7 m.
Then the two cost of widening would be equal to the area of the ring formed between the two circles.
Formula of area of ring is
A = π ( R² - r² )
Where R is the radius of the bigger circle and r is the radius of smaller circle.
Using the formula of circumference, we will now calculate the r.
Circumference = 2 π r
⇒ 330 = 2 × 22/7 × r
⇒ r = 330 × 7/22 × 2
⇒ r = 52.5 m
Now since the circle was widened by 7 m, then the radius of bigger circle is equal to (r+7)
⇒ R = 52.5 + 7 = 59.5 m
Now using the formula of area of ring,
A = π ( R² - r² )
⇒ A = 22/7 × [ (59.5)² - (52.5)² ]
⇒ A = 22/7 × [ 3540.25 - 2756.25 ]
⇒ A = 22 × 784/7
⇒ A = 22 × 112
⇒ A = 2464 m²
Now the cost of widening is ₹8/m²
The cost of widening is equal to Area × cost of widening
⇒ 2464 × 8 = 19712
Hence the final answer is that the cost of widening would be equal to ₹19712
Answer:
the answer is 19712
Step-by-step explanation:
hope my answer help you