Answer:
[tex]112\pi \textsf{or } 351.86 [/tex] cm²
Step-by-step explanation:
The formula for the total surface area ([tex]A[/tex]) of a cylinder is given by:
[tex] A = 2\pi r(r + h) [/tex]
where:
- [tex]r[/tex] is the radius of the cylinder,
- [tex]h[/tex] is the height of the cylinder.
Given that the radius ([tex]r[/tex]) is 4 cm and the height ([tex]h[/tex]) is 10 cm, we can substitute these values into the formula:
[tex] A = 2\pi \times 4(4 + 10) [/tex]
[tex] A = 2\pi \times 4 \times 14 [/tex]
[tex] A = 2 \times 4 \times 14\pi [/tex]
[tex] A = 8 \times 14\pi [/tex]
[tex] A = 112\pi [/tex]
[tex] A = 351.8583772 [/tex]
[tex] A = 351.86 \textsf{ cm$^2$ ( in 2 d.p.)}[/tex]
So, the total surface area of the cylinder is [tex]112\pi \textsf{or } 351.86 [/tex] cm².
