The mass of Tin F is: M_F = 73,472 / a
Let's solve the given problems step-by-step:
1. The surface area of a cylindrical tin can be calculated using the formula for the total surface area:
Surface Area = 2πrh + 2πr²
Since the surface area is proportional to the mass of Tin E, we need more specific measurements of Tin E (such as radius and height) to determine the numerical surface area. For now, we'll call the surface area of Tin E as S_E
2.We know the mass is proportional to the surface area. Let's denote the surface area and mass of Tin E as S_E and M_E, and the surface area and mass of Tin F as S_F and M_F respectively.
Given:
We are given that mass is proportional to surface area, so:
M_E / S_E = M_F / S_F
We need to write the formula for proportionality:
Let k be the proportionality constant, then:
M_E / S_E = k
Similarly, for Tin F:
M_F = k × S_F
To find k:
k = M_E / S_E
Since the units for surface area of Tin E are in terms of π, let's assume S_E to be some constant multiple of π, aπ. Then:
k = 82 / aπ
Replacing k back to find M_F:
M_F = (82 / aπ) × 896π
The π terms cancel out giving:
M_F = (82 × 896) / a
So, the mass of Tin F is:
M_F = 73,472 / a
We have determined the equation to find the mass of Tin F. To find the actual numerical value, we would typically need the actual surface area of Tin E.
A)The total surface area of tin E in terms of π is 82/k.
B)The mass of tin F is k * 896 cm²π
A) Let's assume the mass of the empty cylindrical tin E is m grams, and its surface area is S cm².
According to the given information, the mass of tin E is proportional to its surface area. This can be expressed as:
m ∝ S
Now, we are given that the mass of tin E is 82 grams. Let's say the constant of proportionality is k.
So, m = k * S
We know that the mass of tin E is 82 grams, and its surface area is S. Substituting these values into the equation:
82 = k * S
To find the total surface area of tin E in terms of π, we need to express S in terms of π:
S = 82/k
B) Tin F has a surface area of 896 cm²π.
Since the mass of an empty cylindrical tin is proportional to its surface area, we can use the same constant of proportionality (k) from part A.
Let the mass of tin F be m grams.
m = k * Surface Area of Tin F
m = k * 896 cm²π
Now, to find the mass of tin F, we need to know the value of the constant of proportionality (k). Unfortunately, without additional information or a direct comparison to tin E, we cannot determine the numerical value of k or the exact mass of tin F.
So, we can conclude that the total surface area of tin E in terms of π is 82/k, and the mass of tin F is k * 896 cm²π (with k being an unknown constant of proportionality).
For more questions on total surface area .
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