An 8.5 centimeter green bean pod contains peas that average 0.45 centimeter in diameter. How many peas are in the pod
To calculate the number of peas in the pod, we need to find the volume of the pod and then divide it by the volume of an individual pea.
Step 1: Calculate the volume of the pod.
The volume of a cylinder (like the shape of the pod) is given by the formula V = πr²h, where V is the volume, π is a constant (approximately equal to 3.14159), r is the radius, and h is the height.
Since the pod is in the shape of a cylinder, we need to know the radius and the height.
Given that the average diameter of the peas is 0.45 centimeters, we can find the radius by dividing the diameter by 2.
Radius (r) = 0.45 cm / 2 = 0.225 cm
The height (h) of the pod is given as 8.5 centimeters.
Now, we can plug these values into the volume formula:
V = π(0.225 cm)²(8.5 cm)
Step 2: Calculate the volume of an individual pea.
The volume of a sphere (like the shape of a pea) is given by the formula V = (4/3)πr³, where V is the volume and r is the radius.
To find the radius of the pea, we divide the diameter by 2, just like we did for the pod.
Radius (r) = 0.45 cm / 2 = 0.225 cm
Now, we can plug this value into the volume formula:
V = (4/3)π(0.225 cm)³
Step 3: Divide the volume of the pod by the volume of an individual pea to get the number of peas.
Number of peas = Volume of pod / Volume of pea
Number of peas = π(0.225 cm)²(8.5 cm) / [(4/3)π(0.225 cm)³]
The π(0.225 cm)² cancels out in the numerator and denominator, so the equation simplifies to:
Number of peas = (8.5 cm) / [(4/3)(0.225 cm)]
Now, we can simplify the expression in the denominator:
(4/3)(0.225 cm) = (4/3)(0.225 cm/1) = 0.3 cm
Finally, we can substitute this simplified value back into the equation:
Number of peas = (8.5 cm) / 0.3 cm
Calculating this:
Number of peas = 28.33 peas
So, there are approximately 28 peas in the green bean pod.