find the surface area of the cylinder to the nearest tenth of a square unit

width: 4cm
height: 12.4cm

a: 206cm(2)
b: 623cm (2)
c: 100.5cm (2)
d: 412cm (2)

i think it’s b, can someone give me the right answer quick pls. <3

no that person didnt have a typo

1. C

2. A
3. C
4. D
5. A
6. B
7. C
8. C
For Connexus. 100%

I did that but I can’t remember if I got it right or not🥲… DON’T take my word for it, but heres what I did. I did 3.14 x 4 (the radius not width) ^2. I did 4x4 and got 16. Then I did 3.14 x 16 and got 50.24. The formula is pi(the symbol) r^ 2 h so I multiplied 50.24 by the height 12.4. I got 622.976 and rounded up to 623. Thats what I got but IM NOT SURE if it’s right so pls only take me answer if you don’t mind getting one question wrong!

formula of a cylinders surface area:

2Πrh + 2Πr ^2
OK LETS START

1st part of equation ( 2Πrh )
2 x Π x r x h
2 x 3.14 x 4 x 12.4 =
311.488

2nd part of equation ( 2Πr ^2 )
2 x Π x (r^2)
2 x 3.14 x (4^2)
2 x 3.14 x (16)
6.28 x 16 =
100.48

Now add them:
311.488 +100.48 =
411.968
Round up to 412 <33

Well, well, well, it seems like you're in need of some quick math assistance! Don't worry, I've got your back. The surface area of a cylinder can be calculated using the formula:

Surface Area = 2πrh + 2πr²

In this case, the height of the cylinder is 12.4cm and the radius is half of the width (which is 4cm), so the radius is 2cm.

Now, let's plug in the values:

Surface Area = 2π(2)(12.4) + 2π(2)²

Surface Area ≈ 49.3π + 8π

Surface Area ≈ (49.3 + 8)π

Surface Area ≈ 57.3π

Now, to the nearest tenth, the approximate value of π is 3.1. Multiplying 57.3 by 3.1, we get:

Surface Area ≈ 177.63

So, the correct answer is NOT option b (623cm²), but it is option a (206cm²). Keep in mind, though, that I always encourage a double-check, just to be certain!

To find the surface area of a cylinder, we need to calculate the sum of the areas of the two bases and the lateral surface area.

1. Start by calculating the area of the two circular bases.
The formula to find the area of a circle is A = πr², where r is the radius.
In this case, the radius of the base is half of the width, which is 4cm. So the radius, r, is 4/2 = 2cm.
Therefore, the area of each base is A₁ = π(2cm)² = 4π cm².

2. Next, calculate the lateral surface area.
The lateral surface area of a cylinder is given by the formula A = 2πrh, where r is the radius and h is the height.
In this case, r = 2cm and h = 12.4cm.
So, the lateral surface area is A₂ = 2π(2cm)(12.4cm) = 49.6π cm².

3. Add the areas of the two bases and the lateral surface area to find the total surface area.
Total Surface Area = A₁ + A₁ + A₂ = 4π cm² + 4π cm² + 49.6π cm² = 57.6π cm².

Now, to determine the surface area to the nearest tenth of a square unit, we need to calculate the value of 57.6π and round it to the nearest tenth.
Using a calculator, we can evaluate 57.6π ≈ 180.955 cm².

Comparing this value to the given options:
a: 206 cm²
b: 623 cm²
c: 100.5 cm²
d: 412 cm²

The correct answer is not b because 623 cm² is not the rounded value of 180.955 cm².
Therefore, the correct answer is not b.

why do you think it's b? Did you show some work?

You have the two circular bases, plus the curved lateral area
By width, do you mean diameter? If so, then the radius is 2.
A = 2πr^2 + 2πrh = 2πr(r+h) = 2π*2(2+12.4) = 57.6π = 176

Maybe you have a typo, as that is not one of the choices