Welsh Corgis generally have shoulder heights between 24 and 32 centimeters. Anne wants to compute the corresponding range for the skull size of Welsh Corgis.
She once again uses the formula relating the estimated shoulder height H (in centimeters) of a dog to the internal dimension of the skull D (in cubic centimeters): H space equals space 1.016 D space minus space 31.2.
What is the corresponding minimum skull size for the Welsh Corgi? What is the corresponding maximum skull size for the Welsh Corgi?
To find the corresponding minimum and maximum skull sizes for Welsh Corgis, we can use the given formula: H = 1.016D - 31.2, where H is the shoulder height in centimeters and D is the skull size in cubic centimeters.
Given that the shoulder height range for Welsh Corgis is between 24 and 32 centimeters, we can substitute the minimum and maximum values into the formula to find the corresponding skull sizes.
1. Minimum Skull Size:
Substituting H = 24 into the formula:
24 = 1.016D - 31.2
Add 31.2 to both sides:
24 + 31.2 = 1.016D
55.2 = 1.016D
Divide both sides by 1.016:
D ≈ 54.3316 cubic centimeters
So, the corresponding minimum skull size for Welsh Corgis is approximately 54.33 cubic centimeters.
2. Maximum Skull Size:
Substituting H = 32 into the formula:
32 = 1.016D - 31.2
Add 31.2 to both sides:
32 + 31.2 = 1.016D
63.2 = 1.016D
Divide both sides by 1.016:
D ≈ 62.20 cubic centimeters
So, the corresponding maximum skull size for Welsh Corgis is approximately 62.20 cubic centimeters.