estimate the number of pencil cases needed to hold 10 thousand pennies . Show your work. 2 estimate the height of a stack of 50 thousand pennies . show your work.
Estimate the volume of one penny, but you should probably estimate the size of a small box that a penny would fit into, because when you shove pennies into a box, there's a lot of empty space between the pennies that can't be filled.
The volume of the space occupied by a penny would be d*d*h, where d is it's diameter and h is it's height. (This volume is different than the volume of a penny)
Determine the volume of a pencil case, and divide by the volume + extra space occupied by a penny to determine how many pennies would fit into one pencil box. Then, determine how many pencil boxes you would need.
Stack several pennies together, say 10, and find the height. 50,000 / 10 = ?
Multiply ? by the height of your stack of 10 pennies.
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10 PENCIL CASES I THINK
To estimate the number of pencil cases needed to hold 10,000 pennies, we first need to determine the number of pennies that can fit in a single pencil case. Suppose we assume a standard-sized pencil case.
1. Determine the volume of a penny:
A U.S. penny has a diameter of 0.75 inches and a thickness of 0.06 inches. The volume of a cylindrical penny can be calculated using the formula for the volume of a cylinder: V = πr^2h, where r is the radius and h is the height.
The radius of a penny is half its diameter, so r = 0.75/2 = 0.375 inches.
The height of a penny is 0.06 inches.
Using these values, we can calculate the volume of a penny:
V = π(0.375)^2(0.06) ≈ 0.105 cubic inches.
2. Determine the volume of a pencil case:
Since pencil cases come in various sizes, we need to estimate the average size. Suppose we assume a pencil case with dimensions of 8 inches in length, 2 inches in width, and 1 inch in height.
The volume of the pencil case is:
V = lwh = 8 * 2 * 1 = 16 cubic inches.
3. Calculate the number of pennies a pencil case can hold:
To find out how many pennies a pencil case can hold, divide the volume of the pencil case by the volume of a penny:
16 cubic inches ÷ 0.105 cubic inches = 152.38 ≈ 152 pennies.
Since we cannot have fractional pennies, we can estimate that a pencil case can hold around 152 pennies.
Now, to estimate the number of pencil cases needed for 10,000 pennies, divide the total number of pennies by the number of pennies a single pencil case can hold:
10,000 pennies ÷ 152 pennies ≈ 65.79 ≈ 66 pencil cases.
Therefore, an estimated 66 pencil cases may be needed to hold 10,000 pennies.
Moving on to estimating the height of a stack of 50,000 pennies:
1. Determine the height of a single penny:
We previously found that the height of a penny is 0.06 inches.
2. Calculate the total height of a stack of pennies:
To find out the height of a stack of pennies, multiply the height of a single penny by the total number of pennies:
0.06 inches * 50,000 pennies = 3,000 inches.
Therefore, an estimated stack of 50,000 pennies would have a height of 3,000 inches.