Question

calculate the surface area of the cylinder.
2 ft
1.8 yd
a) 23 ft²
b) 48 ft²
c) 93 ft²
d) 68 ft²

Explanation:

Step1: Convert height to feet

Since 1 yard = 3 feet, then $h = 1.8\times3= 5.4$ ft.

Step2: Recall surface - area formula

The surface - area formula of a cylinder is $A = 2\pi r^{2}+2\pi rh$. Here $r = 2$ ft and $h = 5.4$ ft.

Step3: Calculate area of two bases

The area of one base is $A_{base}=\pi r^{2}=\pi\times2^{2}=4\pi$ ft². The area of two bases is $A_{bases}=2\times4\pi = 8\pi$ ft².

Step4: Calculate lateral - surface area

The lateral - surface area is $A_{lateral}=2\pi rh=2\pi\times2\times5.4 = 21.6\pi$ ft².

Step5: Calculate total surface area

$A=A_{bases}+A_{lateral}=8\pi + 21.6\pi=29.6\pi\approx29.6\times3.14 = 92.944\approx93$ ft².

Answer:

C. 93 ft²