The radii of the larger wheels on a tractor are 32 cm. If the ratio of the diameter of a large to small wheel is 19:7, find the diameters of the smaller wheels
diameter large = 64
diameter small = (7/19) * 64 = 23.58 cm
To find the diameters of the smaller wheels, we need to use the given ratio and the radius of the larger wheels.
Step 1: Convert the ratio of diameters to a ratio of radii by dividing each diameter by 2.
The ratio of diameters (large to small) is 19:7, so the ratio of radii is 19/2 : 7/2.
Step 2: Set up a proportion to find the unknown radius of the smaller wheels:
(large wheel radius) / (small wheel radius) = (large wheel diameter) / (small wheel diameter)
Let's assign the unknown radius of the smaller wheels as 'x':
32 cm / x = (19/2) / (7/2)
Step 3: Solve the proportion for 'x' (the radius of the smaller wheel).
First, simplify the equation by canceling the common factors:
32 / x = 19 / 7
Second, cross-multiply:
7 * 32 = 19 * x
Step 4: Solve for 'x':
224 = 19x
Divide both sides of the equation by 19:
x = 224 / 19
The radius of the smaller wheels is 224/19 cm.
Step 5: To find the diameter of the smaller wheels, multiply the radius by 2:
Diameter = 2 * Radius.
Therefore, the diameter of the smaller wheels is:
2 * (224/19) cm = 448/19 cm (approx. 23.579 cm).