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✒️FINDING SURFACE AREA

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[tex]\large\underline{\mathbb{QUESTION}:}[/tex]

Find the surface area of the cylinder? Where ​ ≈ 3.14

[tex]\large\underline{\mathbb{ANSWER}:}[/tex]

  • 904.32 square yards

[tex]\large\underline{\mathbb{SOLUTION}:}[/tex]

Surface area of a cylinder:

  • Surface area = [tex]\sf \: A_t_o_p + A_b_o_t_t_o_m+ A_s_i_d_e[/tex]

Find the radius and height of the cylinder.

  • radius = 9
  • height = 7

Find the area of the circle on the top of the cylinder. Use 3.14 for ​.

[tex]\sf \:A_t_o_p[/tex] = r²

  • ≈ 3.14 × 9 × 9
  • ≈ 254.34

The circle on the bottom of the cylinder is the same on the top, so:

  • [tex]\sf \: A_b_o_t_t_o_m = A_t_o_p[/tex] ≈ 254.34

Find the circumference of the top circle.

C =  2​r

  • ≈ 2 × 3.14 × 9
  • ≈ 56.52

Now find the area of the curved surface. The curved surface is a rectangle. One side length is the height, and the other side length is the circumfrence of the circle.

Aside = C × h

  • ≈ 56.52 × 7
  • ≈ 395.64

Now add the areas to find the surface area of the cylinder.

Surface area

  • = [tex]\sf \: A_t_o_p + A_b_o_t_t_o_m+ A_s_i_d_e[/tex]
  • ≈ 254.34 + 254.34 + 395.64
  • ≈ 904.32

The surface area of the cylinder is about 904.32 square yards.

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