Question
Aleksandr has a roll of paper that is in the shape of a right circular cylinder. It has a height of 28 cm and a diameter of 15.5 cm. Help Aleksandr solve for the surface area. Use 3.14 for π .(1 point)
Responses
A). 1,508.77 cm2
1,508.77 cm squared
B). 1,362.76 cm2
1,362.76 cm squared
C). 4,234.29 cm2
4,234.29 cm squared
D). 1,739.95 cm2
Responses
A). 1,508.77 cm2
1,508.77 cm squared
B). 1,362.76 cm2
1,362.76 cm squared
C). 4,234.29 cm2
4,234.29 cm squared
D). 1,739.95 cm2
Answers
GPT 3.5
The formula for the surface area of a cylinder is 2πrh + 2πr^2, where r is the radius and h is the height.
Given that the diameter is 15.5 cm, the radius is half of that, so r = 15.5 / 2 = 7.75 cm.
Substitute the values into the formula:
Surface area = 2 * 3.14 * 7.75 * 28 + 2 * 3.14 * 7.75^2
Surface area = 2 * 3.14 * 217 + 2 * 3.14 * 60.0625
Surface area = 6.28 * 217 + 6.28 * 60.0625
Surface area = 1,336.76 + 376.1375
Surface area = 1,712.8975 cm^2
Therefore, the closest answer is:
B). 1,362.76 cm^2
1,362.76 cm squared
Given that the diameter is 15.5 cm, the radius is half of that, so r = 15.5 / 2 = 7.75 cm.
Substitute the values into the formula:
Surface area = 2 * 3.14 * 7.75 * 28 + 2 * 3.14 * 7.75^2
Surface area = 2 * 3.14 * 217 + 2 * 3.14 * 60.0625
Surface area = 6.28 * 217 + 6.28 * 60.0625
Surface area = 1,336.76 + 376.1375
Surface area = 1,712.8975 cm^2
Therefore, the closest answer is:
B). 1,362.76 cm^2
1,362.76 cm squared