Question

determining the surface area of a cylinder
the radius of a cylinder is 4 inches and the height is 5 inches. which statements are correct? check all that apply.
☐ the area of the two bases is 16π in².
☐ the area of the two bases is 32π in².
☐ the lateral area is 40π in².
☐ the lateral area is 72π in².
☐ the total surface area is 72π in².

Explanation:

Step1: Calculate area of two bases

A cylinder's bases are circles. Area of one base: $\pi r^2 = \pi (4)^2 = 16\pi$. For two bases: $2 \times 16\pi = 32\pi$ in².

Step2: Calculate lateral surface area

Lateral area formula: $2\pi r h$. Substitute values: $2\pi \times 4 \times 5 = 40\pi$ in².

Step3: Calculate total surface area

Total area = 2 bases area + lateral area: $32\pi + 40\pi = 72\pi$ in².

Step4: Match with given statements

Compare calculated values to the options provided.

Answer:

• The area of the two bases is $32\pi$ in².
• The lateral area is $40\pi$ in².
• The total surface area is $72\pi$ in².