Question

answer questions 8 - 10 and be sure to show all work.

1. find the lateral surface area of the cylinder to the nearest hundredth.

image of a cylinder with length 9.5 cm and radius 2 cm

1. find the total surface area of the cylinder to the nearest hundredth.

image of a cylinder with diameter 19 mm and height 21 mm

1. a cylindrical can has a height of 5.5 inches and a diameter of 4.5 inches. find the lateral and total surface area of the can. round your answers to the nearest tenth.

image of a cylindrical can
lateral surface area:
total surface area:

Explanation:

Step1: Define lateral surface area formula

Lateral Surface Area (LSA) of cylinder: $LSA = 2\pi rh$

Step2: Plug in values for Q8

$r=2\ \text{cm}$, $h=9.5\ \text{cm}$
$LSA = 2\pi(2)(9.5) = 38\pi \approx 119.38\ \text{cm}^2$

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Step1: Define total surface area formula

Total Surface Area (TSA) of cylinder: $TSA = 2\pi r(r+h)$

Step2: Calculate radius for Q9

Diameter = 19 mm, so $r=\frac{19}{2}=9.5\ \text{mm}$, $h=21\ \text{mm}$

Step3: Compute TSA for Q9

$TSA = 2\pi(9.5)(9.5+21) = 2\pi(9.5)(30.5) = 579.5\pi \approx 1820.53\ \text{mm}^2$

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Step1: Find radius for Q10

Diameter = 4.5 inches, so $r=\frac{4.5}{2}=2.25\ \text{in}$, $h=5.5\ \text{in}$

Step2: Compute lateral surface area for Q10

$LSA = 2\pi(2.25)(5.5) = 24.75\pi \approx 77.7\ \text{in}^2$

Step3: Compute total surface area for Q10

$TSA = 2\pi(2.25)(2.25+5.5) = 2\pi(2.25)(7.75) = 34.875\pi \approx 109.6\ \text{in}^2$

Answer:

1. $\boldsymbol{119.38\ \text{cm}^2}$
2. $\boldsymbol{1820.53\ \text{mm}^2}$
3. Lateral surface area: $\boldsymbol{77.7\ \text{in}^2}$

Total surface area: $\boldsymbol{109.6\ \text{in}^2}$