Claim: the lateral (side ) surface of any area of any cylinder can is larger than the circlar surface area of its bottom. Which of the following is an example showing that the claim is false?
a. a can with the diameter of 5 inches and height of 10 inches
b. a can with diameter 1 inch and height 10 inches
c. a can with the diameter 10 inches and height of 2 inches
d. a can with diameter 10 inches and height of 10 inches.
geometry- need help - Ms. Sue, Wednesday, May 25, 2011 at 11:44am
The diameter must be much greater than the height.
Mary ??
C would be a false claim then ?
Right.
Thank you!! This has been a rough day in geometry
To determine if the claim is false, we need to compare the lateral surface area of the cylinder with the circular surface area of its bottom.
The lateral surface area of a cylinder can be found using the formula: A_lateral = 2πrh, where r is the radius of the base and h is the height of the cylinder.
The circular surface area of the bottom (also called the base) of a cylinder can be found using the formula: A_base = πr^2, where r is the radius of the base.
Let's go through each option and calculate:
a. a can with the diameter of 5 inches and height of 10 inches:
For this option, the radius would be 5/2 = 2.5 inches.
A_lateral = 2πrh = 2π(2.5)(10) = 50π square inches
A_base = πr^2 = π(2.5^2) = 6.25π square inches
b. a can with diameter 1 inch and height 10 inches:
For this option, the radius would be 1/2 = 0.5 inches.
A_lateral = 2πrh = 2π(0.5)(10) = 10π square inches
A_base = πr^2 = π(0.5^2) = 0.25π square inches
c. a can with the diameter 10 inches and height of 2 inches:
For this option, the radius would be 10/2 = 5 inches.
A_lateral = 2πrh = 2π(5)(2) = 20π square inches
A_base = πr^2 = π(5^2) = 25π square inches
d. a can with diameter 10 inches and height of 10 inches:
For this option, the radius would be 10/2 = 5 inches.
A_lateral = 2πrh = 2π(5)(10) = 100π square inches
A_base = πr^2 = π(5^2) = 25π square inches
From the calculations, we can see that for option c, the lateral surface area of the cylinder is smaller than the circular surface area of its bottom (A_lateral < A_base). Hence, option c is an example showing that the claim is false.