Question

Find the lateral and surface area of the cylinder whose diameter is 4.2 meters and has a height of 7.8 meters. Please help due today and please show work

Answer 1

Hi, I presume you're asking for the surface area of the entire cylinder, which includes the top area (circle), base area (also a circle), and the curved surface of the cylinder.

Surface area of cylinder
= 2 × (Area of circle) + Curved surface area

Formula of area of circle is:
$\pi {r}^{2}$
or pie × radius^2

Radius of circle is half the diameter of circle:
Radius = 4.2 ÷ 2
= 2.1 meters OR 2.1 m ("m" is written as the short form of meters)

Area of 1 circle = pie × radius^2
= pie × 2.1^2
<Type (2.1^2) OR (2.1 × 2.1) into calculator>
= 4.41 × pie
$= 4.41\pi$
If you'd like to do mental sums, simply change the decimal into a fraction: 21/10. Your Numerator will be 21^2 and denominator will be 10^2. Then you'll get 441/100, which is 4.41.

To find curved surface area of cylinder, imagine you have many hola-hoops that are of the same size, and you stack them all up on top of each other. You will eventually form a cylinder that is hollow on the inside. A hola-hoop in this example is the circumference of your circle, and the hola-hoops being piled up is your curved surface area. The number of hola-hoops tell you the height of your hollow cylinder.

Circumference of circle has a formula of:
$2\pi \times r \\ = \pi \times d$
"d" stands for diameter of circle.

Thus, Curved surface area
= Circumference × Height
= pie × 4.2 × 7.8
<Type into calculator>
= 32.76pie

Finally, the surface area of cylinder is:
2 × Area of circle + Curved surface area
= 2 × 4.41pie + 32.76pie
= 8.82pie + 32.76pie
= 41.58pie m^2
("m^2" is the unit for area where meters is involved)

Hope this helps! :)

Answer 2

$\pi {r}^{2} h$