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
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. I don't know.
2. A=2πrh+2πr^2
A = (2 * 3.14 * 8 * 16) + (2 * 3.14 * 64)
A = 803.84 + 401.92
Please post the last two questions as a New Question.
#3 using #2, (B)
#4 A=πdh=125.6 so, (C)
#5 lateral area is circumference * height = 2πrh
For the first question, the altitude of the cylinder from point B to point C is represented by a line. So the correct answer is A. Line BC. The altitude is the distance between the two points measured perpendicular to the bases of the cylinder.
For the second question, to find the total surface area of a cylinder, we need to calculate the lateral surface area (the area of the curved side) and the area of the two bases. The formula for the lateral surface area of a cylinder is given by the product of the height and the circumference of the base, which can be written as 2πrh. The formula for the area of the base (a circle) is πr^2.
Given the radius as 8 cm and the height as 16 cm, we can calculate the lateral surface area using the formula: 2π(8 cm)(16 cm) = 256π cm^2. The area of one base is π(8 cm)^2 = 64π cm^2. Since we have two bases, the total area of the bases is 2(64π cm^2) = 128π cm^2. Adding the lateral surface area and the area of the bases, we get 256π cm^2 + 128π cm^2 = 384π cm^2. Therefore, the correct answer is C. 384π cm^2.
For the third question, we need to approximate the total surface area of the cylinder. The formula for the lateral surface area is the same as before: 2πrh. Given the radius as 22 cm and the width (which is probably referring to the height) as 9 cm, we can calculate the lateral surface area using the formula: 2π(22 cm)(9 cm) = 396π cm^2. However, since we are asked for the best approximation, we need to round the result to the nearest whole number. The nearest whole number to 396 is 400. Therefore, the approximate lateral surface area is 400 cm^2. The correct answer is D. 1070 cm^2.
For the fourth question, we need to find the amount of paper needed to create a label for the lateral surface of the cylinder. The lateral area is the same as the lateral surface area we calculated before, 2πrh. Given the diameter as 5 inches (which means the radius is 2.5 inches) and the height as 8 inches, we can calculate the lateral surface area using the formula: 2π(2.5 inches)(8 inches) = 40π inches^2. However, since we are asked for an approximation, we can use the value of π as approximately 3.14. Therefore, the approximate lateral surface area is 40π inches^2 ≈ 40(3.14) inches^2 ≈ 125.6 inches^2. The closest approximation provided is A. about 39.3 inches^2.
Regarding the last question, the lateral area of a cylinder is given by the formula 2πrh. The correct answer is C. 2πrh. This formula calculates the area of the curved side of the cylinder, which is the lateral area.