Question

mini - quiz
solve each question below and round solutions to the nearest hundredth.
find the lateral and total surface area of the cylinder.
(image of a cylinder with height 75 mm and radius 20 mm)

1. lateral surface area:
2. total surface area:

(image of a cylinder with height 13.5 cm and diameter 12 cm)
find the lateral and total surface area of the cylinder.

1. lateral surface area:
2. total surface area:
3. spot’s cylindrical dog bowl is silver on the inside surfaces and red on the exterior. the bowl has a diameter of 8 inches and a height of 5.7 inches. find the surface area of the bowl covered by silver.

(image of a dog house)

Explanation:

Step1: Calculate first cylinder lateral area

Formula: $LSA = 2\pi rh$, $r=20$ mm, $h=75$ mm
$LSA = 2\pi(20)(75) = 3000\pi \approx 9424.78$

Step2: Calculate first cylinder total area

Formula: $TSA = 2\pi rh + 2\pi r^2$
$TSA = 3000\pi + 2\pi(20)^2 = 3000\pi + 800\pi = 3800\pi \approx 11938.05$

Step3: Calculate second cylinder lateral area

Formula: $LSA = 2\pi rh$, $r=\frac{12}{2}=6$ cm, $h=13.5$ cm
$LSA = 2\pi(6)(13.5) = 162\pi \approx 508.94$

Step4: Calculate second cylinder total area

Formula: $TSA = 2\pi rh + 2\pi r^2$
$TSA = 162\pi + 2\pi(6)^2 = 162\pi + 72\pi = 234\pi \approx 735.13$

Step5: Calculate dog bowl silver surface area

Area = lateral area + base area: $2\pi rh + \pi r^2$, $r=\frac{8}{2}=4$ in, $h=5.7$ in
$Area = 2\pi(4)(5.7) + \pi(4)^2 = 45.6\pi + 16\pi = 61.6\pi \approx 193.52$

Answer:

1. Lateral surface area: $9424.78$ mm²
2. Total surface area: $11938.05$ mm²
3. Lateral surface area: $508.94$ cm²
4. Total surface area: $735.13$ cm²
5. Surface area of silver-covered part: $193.52$ in²