I was wondering if you can help me with math real quickly. I just cant figure this out.

For the first question I have to find the surface area for the given cylinder. I have to use 3.14 and round to the nearest whole number. The radius is 6ft and the height is 20 ft.

A. 180 ft2
B. 720 ft2
C. 433 ft2
D. 135 ft2

For the second question I have to find the lateral area for the given cylinder. I have to use 3.14 and round to the nearest whole number. The radius is 6 yd, and the height is 24 yds.

A. 144 yd2
B. 288 yd2
C. 2,712 yd2
D. 904 yd2

No matter how much I work on the problems I still cant get the right answer. Can you please help? Thanks.

Imagine "opening up" a cylinder, what would you get?

2 equal circles + a rectangle whose length is the circumference of the circle and whose height is the height of the cylinder.

so SA = 2π(6^2) + 2π(6)(20)
= 72π + 240π = 312π = appr 980
No wonder you can't figure it out, none of the answers are correct

for the 2nd:
SA = 2π(6^2) + 2π(6)(24)
= 72π + 288π = 360π = appr 1131

Are these the answers you got?

a = 2pi*r(r+h) = 2pi*6*26 = 979.68

Hmmm. That includes both ends. The lateral area is
a = 2pi*r*h = 2pi*6*20 = 753.6
Is there a typo somewhere?

2pi*6*24 = 904.3, so (D)

@Reniy: Yes those were the answers I came up with. I couldn't figure out what I was doing wrong, turns out I was doing the first one right and the second one was a bit off. Thank you for the help.

@Steve: Thank you for the help as well, no there isn't a typo. Sometimes the math we're doing is quite confusing. Thank you for the help. c:

Of course, I can help you with those math problems! Let's start with the first question:

To find the surface area of a cylinder, we need to calculate the area of the two bases and the lateral surface area (which wraps around the sides).

1. Start by finding the area of the two bases. The formula for the area of a circle is A = πr^2, where A represents the area and r represents the radius.

For the first question, the radius is given as 6ft. So, the area of one base is A1 = 3.14 * (6ft)^2.

2. Next, calculate the lateral surface area. The formula for the lateral surface area of a cylinder is A = 2πrh, where r is the radius and h is the height.

For the first question, the radius is 6ft, and the height is given as 20ft. So, the lateral surface area is A2 = 2 * 3.14 * 6ft * 20ft.

3. Finally, calculate the total surface area by adding the two bases' area and the lateral surface area:

Total surface area = A1 + A1 + A2.

Using the given values:
Total surface area = 2 * 3.14 * (6ft)^2 + 2 * 3.14 * 6ft * 20ft.

Now, you can calculate the total surface area using your calculator or simplifying the equation. Once you have the numerical answer, round it to the nearest whole number and compare it to the options provided in the question. The corresponding option will be the correct answer.

Now, let's move on to the second question:

To find the lateral area of a cylinder, we only need to calculate the area of the lateral surface (the part that wraps around the sides).

1. The formula for the lateral surface area is the same as before: A = 2πrh, where r is the radius and h is the height.

For the second question, the radius is given as 6yd, and the height is given as 24yd. So, the lateral surface area is A = 2 * 3.14 * 6yd * 24yd.

2. Calculate the lateral surface area using your calculator or simplifying the equation.

Once you have the numerical answer, round it to the nearest whole number and compare it to the options provided in the question. The corresponding option will be the correct answer.

Remember to use the value of π as 3.14 as instructed.

I hope this helps you solve the math problems!