Question

calculate the surface area of the right cylinder, to the nearest square foot. a) 23 ft2 b) 68 ft2 c) 48 ft2 d) 93 ft2 1.8 yd 2 ft

Explanation:

Step1: Convert height to feet

Since 1 yard = 3 feet, and the height of the cylinder is 1.8 yards. So the height $h$ in feet is $h = 1.8\times3=5.4$ feet. The radius $r = 2$ feet.

Step2: Recall surface - area formula

The surface - area formula of a cylinder is $S = 2\pi r^{2}+2\pi rh$.

Step3: Calculate the area of the two bases

The area of one base is $A_{base}=\pi r^{2}$. Substituting $r = 2$ feet, we get $A_{base}=\pi\times(2)^{2}=4\pi$ square feet. The area of the two bases is $A_{2bases}=2\times4\pi = 8\pi$ square feet.

Step4: Calculate the lateral - surface area

The lateral - surface area formula is $A_{lateral}=2\pi rh$. Substituting $r = 2$ feet and $h = 5.4$ feet, we get $A_{lateral}=2\pi\times2\times5.4 = 21.6\pi$ square feet.

Step5: Calculate the total surface area

$S=A_{2bases}+A_{lateral}=8\pi + 21.6\pi=29.6\pi$ square feet.

Step6: Approximate the value

$S\approx29.6\times3.14 = 92.944\approx93$ square feet.

Answer:

d) 93 ft²