Question
I need the answers for math unit six surface area, lesson nine surface area of cylinders quick check, five questions
Answers
GPT 3.5
1. What is the formula for finding the surface area of a cylinder?
Answer: The formula for finding the surface area of a cylinder is SA = 2πr^2 + 2πrh, where r is the radius and h is the height of the cylinder.
2. If the radius of a cylinder is 5 inches and the height is 10 inches, what is the surface area of the cylinder?
Answer: SA = 2π(5)^2 + 2π(5)(10) = 2π(25) + 2π(50) = 50π + 100π = 150π square inches
3. A cylinder has a surface area of 100 square centimeters. If the radius is 3 centimeters, what is the height of the cylinder?
Answer: 100 = 2π(3)^2 + 2π(3)h
100 = 18π + 6πh
100 = 24π + 6πh
24π = 6πh
h = 4 centimeters
4. If the height of a cylinder is double its radius, what is the surface area of the cylinder?
Answer: Let the radius be r, then the height is 2r.
SA = 2πr^2 + 2πr(2r) = 2πr^2 + 4πr^2 = 6πr^2
5. If the surface area of a cylinder is 200 square units and the radius is 4 units, what is the height of the cylinder?
Answer: 200 = 2π(4)^2 + 2π(4)h
200 = 32π + 8πh
200 = 40π + 8πh
40π = 8πh
h = 5 units
Answer: The formula for finding the surface area of a cylinder is SA = 2πr^2 + 2πrh, where r is the radius and h is the height of the cylinder.
2. If the radius of a cylinder is 5 inches and the height is 10 inches, what is the surface area of the cylinder?
Answer: SA = 2π(5)^2 + 2π(5)(10) = 2π(25) + 2π(50) = 50π + 100π = 150π square inches
3. A cylinder has a surface area of 100 square centimeters. If the radius is 3 centimeters, what is the height of the cylinder?
Answer: 100 = 2π(3)^2 + 2π(3)h
100 = 18π + 6πh
100 = 24π + 6πh
24π = 6πh
h = 4 centimeters
4. If the height of a cylinder is double its radius, what is the surface area of the cylinder?
Answer: Let the radius be r, then the height is 2r.
SA = 2πr^2 + 2πr(2r) = 2πr^2 + 4πr^2 = 6πr^2
5. If the surface area of a cylinder is 200 square units and the radius is 4 units, what is the height of the cylinder?
Answer: 200 = 2π(4)^2 + 2π(4)h
200 = 32π + 8πh
200 = 40π + 8πh
40π = 8πh
h = 5 units