On My scooter, the rear wheel's diameter is 6 cm more than the front wheel's. The rear wheel's circumference is ___ cm more than the front wheel's.
A) 3π B) 6π C) 9π D) 36 π
π(d+6) = πd + 6π
front wheel's circumference = d π
rear wheel's circumference = ( d + 6 ) π
( d + 6 ) π - d π =
π ∙ d + π ∙ 6 - d π =
d ∙ π + 6 ∙ π - d π =
d π - d π + 6 ∙ π = 6 π
thx
To find the circumference of a circle, we use the formula C = 2πr, where C is the circumference and r is the radius of the circle.
Let's assume the radius of the front wheel is r. Since the diameter is twice the radius, the diameter of the front wheel is 2r.
Given that the rear wheel's diameter is 6 cm more than the front wheel's, the diameter of the rear wheel is 2r + 6 cm.
The radius of the rear wheel is half its diameter, so the radius of the rear wheel is (2r + 6) / 2 = r + 3 cm.
Now, we can calculate the circumference of both wheels:
For the front wheel: C_front = 2πr.
For the rear wheel: C_rear = 2π(r + 3).
To find the difference in circumference between the two wheels, we subtract the front wheel's circumference from the rear wheel's circumference: C_rear - C_front = 2π(r + 3) - 2πr.
Applying the distributive property, we get: C_rear - C_front = 2πr + 6π - 2πr.
Simplifying the equation, we find: C_rear - C_front = 6π.
Therefore, the rear wheel's circumference is 6π cm more than the front wheel's circumference.
The correct answer is B) 6π.