What is the altitude of this cylinder: B ==> C?
A. line BC
B. segment BC
C. ray BC
D. Point BC
MY ANSWER: A. Line BC
What is the total surface area of this cylinder?
Radius = 8 cm
Height = 16 cm
A. 128 pi cm^2
B. 256 pi cm^2
C. 384 pi cm^2
D. 1024 pi cm^2
MY ANSWER: C. 384 pi cm^2
What is the best approximation of the total surface area of this cylinder?
Radius = 22 cm
Width? = 9 cm
A. 1380 cm^2
B. 4280 cm^2
C. 2140 cm^2
D. 1070 cm^2
MY ANSWER: D. 1070 cm^2
A cylindrical container's lateral surface is to be covered by a label. The container's diameter is 5 inches and its height is 8 inches. How much paper is needed to create the label?
A. about 39.3 in^2
B. about 82.5 in^2
C. about 126 in^2
D. about 165 in^2
In the surface area formula for a cylinder with radius r and height h, what is the lateral area?
A. 2 (pi) r^2
B. pi rh
C. 2 (pi) rh
D. r^2
MY ANSWER: A. 2 (pi) r^2
Thank you Ms. Sue for helping me!
1. What is the altitude of this cylinder: B ==> C?
ANSWER = B
2. What is the total surface area of this cylinder?
ANSWER = C
3. What is the best approximation of the total surface area of this cylinder?
ANSWER = A
4. A cylindrical container's lateral surface is to be covered by a label. The container's diameter is 5 inches and its height is 8 inches. How much paper is needed to create the label?
ANSWER = C
5. In the surface area formula for a cylinder with radius r and height h, what is the lateral area?
ANSWER = C
You're welcome! I'm glad I could help. However, I want to point out a mistake in your first answer. The altitude of a cylinder refers to the distance between the bases of the cylinder. In this case, the altitude of the cylinder would be the distance between points B and C. However, from the given options, none of them accurately represents the altitude of a cylinder. So, there is no correct answer among the options provided.
Moving on to your second question, to find the total surface area of a cylinder, you need to add the areas of the two bases and the lateral surface area. The formula for the total surface area of a cylinder is 2πr^2 + 2πrh, where r is the radius and h is the height.
Plugging in the given values:
Radius = 8 cm
Height = 16 cm
Total surface area = 2π(8^2) + 2π(8)(16)
= 128π + 256π
= 384π cm^2
So, your answer C, 384π cm^2, is correct.
Now, let's move on to your third question. To find the best approximation of the total surface area of a cylinder, we need to use the same formula as before: 2πr^2 + 2πrh.
Plugging in the given values:
Radius = 22 cm
Width (which I believe should be the height) = 9 cm
Total surface area ≈ 2π(22^2) + 2π(22)(9)
≈ 968π + 396π
≈ 1364π cm^2
To approximate the total surface area, we can use the approximation π ≈ 3.14:
Total surface area ≈ 1364(3.14) cm^2
≈ 4285.36 cm^2
Rounded to the nearest whole number, the best approximation is 4285 cm^2. So, answer option B, 4280 cm^2, is the closest approximation.
Lastly, let's tackle your last question about the amount of paper needed to create a label for a cylindrical container. The formula for the lateral surface area (or the area of the label) of a cylinder is 2πrh, where r is the radius and h is the height.
Plugging in the given values:
Diameter = 5 inches (which means the radius is 2.5 inches)
Height = 8 inches
Lateral surface area = 2π(2.5)(8)
= 40π in^2
To approximate the lateral surface area, we can use the approximation π ≈ 3.14:
Lateral surface area ≈ 40(3.14) in^2
≈ 125.6 in^2
Rounded to the nearest tenth, the approximate amount of paper needed is about 125.6 in^2. So, the closest answer option is A, about 39.3 in^2.
I hope this explanation clarifies everything! Let me know if you have any further questions.