The diameter of a soup can is 7cm. The label wraps around the can. About how many centimeters long must the label be to go all the way around the soup can?(use 22/7 for pi) explain how to mentally check whether your answer is reasonable.
the diameter of a soup can is about 7 cm. about how many cm long must the lable be to go all the way around the soup can?
circumference = 2πr or dπ
= 6π
= ..
good grief, who still uses 22/7 for π ??
Well, since the label goes all the way around the can, we need to find the circumference of the can. The formula for circumference is C = πd, where C is the circumference and d is the diameter.
Let's plug in the given values. The diameter is 7cm, so the formula becomes C = (22/7) * 7.
To mentally check if our answer is reasonable, we can compare it to the diameter. If the circumference is significantly smaller than the diameter, that would be pretty funny! It would mean that the label can't even go around once.
On the other hand, if the circumference is much larger than the diameter, well, that would also be amusing! It would mean that the label could go around several times, creating quite a fashion statement on the soup can.
But let's get to the actual calculation. C = (22/7) * 7 simplifies to C = 22.
So, the label must be 22 centimeters long to go all the way around the soup can. And mentally, we can check that it seems like a reasonable answer, as the label will be able to wrap around once comfortably without any funny business!
To calculate the length of the label required to go all the way around the soup can, we need to find the circumference of the can. The circumference is given by the formula:
C = πd
where C is the circumference and d is the diameter. In this case, the diameter of the soup can is 7cm, so we can substitute it into the formula:
C = (22/7) * 7 = 22cm
So, the length of the label must be approximately 22cm in order to go all the way around the soup can.
To mentally check the reasonableness of the answer, we can imagine a circle with a diameter of 7cm. We know that the circumference of any circle is a little more than three times its diameter. In this case, we are using the approximate value of π as 22/7. Since 22/7 is a little more than 3, we can expect the circumference to be a little more than three times the diameter, which is reasonable. Additionally, the diameter of the soup can is 7cm, and the length of the label is approximately 22cm, which means the label needs to wrap around the can a little more than three times. This also confirms that the answer is reasonable.