Use the image to answer the question.
An oblique cylinder is labeled with a height of 15 centimeters and radius 5 centimeters.
Find the surface area of the cylinder below. Use the approximation 3.14 for pi.
(1 point)
Responses
628 centimeters
628 centimeters
1,099 square centimeters
1,099 square centimeters
628 square centimeters
628 square centimeters
533.8 square centimeters
To find the surface area of the oblique cylinder, we need to find the area of the two bases and the lateral area.
The area of each base can be calculated using the formula for the area of a circle: A = πr², where r is the radius.
In this case, the radius is 5 centimeters, so the base area is:
A_base = 3.14 * (5)^2 = 3.14 * 25 = 78.5 square centimeters.
The lateral area of the cylinder can be calculated by finding the circumference of each base, then multiplying it by the height of the cylinder.
The circumference of a circle can be calculated using the formula: C = 2πr.
For the lower base (oblique), the circumference is:
C_lower = 2 * 3.14 * 5 = 31.4 centimeters.
The lateral area of the oblique part of the cylinder is the circumference multiplied by the height:
Lateral_area_oblique = C_lower * height = 31.4 * 15 = 471 square centimeters.
Adding the area of the two bases and the lateral area, we get the total surface area of the cylinder:
Surface_area = 2 * A_base + Lateral_area_oblique
= 2 * 78.5 + 471
= 157 + 471
= 628 square centimeters.
Therefore, the correct answer is 628 square centimeters.